How viable is it? I love archery, but I get bored with sneaking and sniping my way through everything. I would allow myself only one sneak attack per battle. After that I would have to get out of sneak mode and start firing arrows. Light armor, archery, alchemy. Is it doable?

Approved. Please proceed.

I think you'll end up doing a lot of running back and forth and side to side. Since archery is a purely ranged skill, it's less viable when a group of enemies is running right at you. You lose your distance advantage. I often play a stealthy archer, though there are quite a few times where my hiding wasn't good enough, and I ended up with a hole group of bandits running straight at me. Either I could stop using my bow in favour of a dagger or sword or other melee weapon, or I could continue using my bow while running backwards to try to keep some bit of an advantage. It's doable, but I don't know if doing that all the time would be all that enjoyable.

EDIT: If you choose to also be skilled in melee combat, then yeah, non-sneak archery is fine.

i actually enjoy my game play with non-sneak archery more than sneak archery, but I mix it with melee in case they get close. I have played the following:

Illusionist - Necro
* Primary: bow
* Support: illusion frenzy/calm + necro tanks
p.s. if you want an army, hire someone like Janessa, give her staff of summoning. you can have one big army for you. This is very strong build

Archery - Duelist
* Primary: bow
* Support: dual wield
fight style pretty much start shooting enemy from distance, if they come close then use dual wield power attack to stagger them and slash them hard. suggest to add Elemental fury for the extra fun

If you really really want to go pure archery, it also work but you need to constantly running around for kiting. using poison for slow is recommended too, but against someone immune to poison you will have harder time. also bow bash can give you some breathing room

At first, a pure archer is pretty much suicidal. It gets easier with power shot (which you can get very early by exploiting Faendal's naive kindness in giving free training), but is still tough. Once you have Quick Draw, Steady Hand and Ranger, it becomes about as easy as any other form of combat. Just run about firing arrows like you're holding some weird kinda machine gun.

One note on this kind of build. As you level up, you'll want to upgrade your bow... Until you get your enchanting to 100 (if you use enchanting at all it's gotta happen eventually as you upgrade your gear) and take the perks on the left branch of the tree. Then you'll want to revert to an enchanted longbow, because it fires much more often; The arrows are slower, but if you're not sneaking about you'll want that constant stagger it provides, and the DPS is great with an enchantment.

Archers excel at ranged combat, obviously, but even they have to be prepared for melee combat.

True that, use a dagger at least. Legolas style.

Quick Shot, Overdraw, Power Shot and Ranger all make Archery highly viable without Sneak, but you'll struggle before getting those I think, since you'll be far too slow and cumbersome as soon as more than one enemy rushes towards you.

Pure archer in the playing style that he describes is not pure suicide at all, if the first shot is done in stealth for the sneak dmg bonus. Taking a companion with you in the beginning that uses melee and takes the first punches of a battle, while the archer assists from the rear.
If you allow 1 stealth shot per battle, it often means you kill the first target and so the chances turn more into your favor.

I play a similar build. I will open with a sneak attack or two, but I avoid running away just to get in another sneak attack.

Things that help:

Power Shot. Stagger is great for giving you extra time to get in a shot, and to prevent the enemy from hitting you.
Ranger. More maneuverability against ranged enemies.
Quick Shot. Higher DPS when not sneak-attacking.
Slow potions. Again, gives you more time to get in a shot without the enemy hitting you.

Things that help a little bit less:

Alchemy in general. I play a non-enchanting character (I'll use the odd enchanted item I find, but I don't do any of my own enchanting). Alchemy is great for a variety of effects: restore health/stamina; fortify marksman; poison; resist fire/frost/shock.
Light Armour perks. I guess skillful players will get away with not needing these, because they'll be too good at avoiding enemy damage. I'm not so skillful, so I need some extra protection. But (i) it's in character for me, and (ii) I'm not using the perks elsewhere anyway.
Smithing. I don't grind this, nor exploit the enchanting/alchemy loop. But a bit of extra damage/armour is useful. Especially when you use sneak attacks or fortify marksman potions.
Bullseye. Doesn't work often enough to make it worth relying on, but it's still worth getting.

I'm going for a 1:1 ratio of health:stamina when I level up. (No magicka). I play on Adept. It's enough of a challenge for me.

Other general advice: I like to avoid leveling up my support skills too much early on. I basically just use archery, with a little bit of sneak, until my archery is at least 50 or 60. I find that Sneak pretty much keeps pace with Archery if you don't try to sneak attack every enemy. Then I start to slowly increase alchemy and smithing. (Light Armour increases at a decent rate anyway; Speech and Lockpicking will also inevitably increase slowly). This just means that early on my ability to deal and take damage keeps pace with the leveled enemies I encounter. Later on as my damage and armour plateau, I need to start being more tactical, and that's where potions start to play a bigger role. By that time I've also built up enough of a stockpile of reagents that I can continually churn out a good amount of useful potions (slow; restore health/stamina; fortify marksman; resist fire/frost/shock; poison).

Edit: forgot to mention, I don't use any melee weapons at all. Strictly bows only.

I like this playstyle, and what gets me by in tough fights is knowing the land and where I can stand out of melee range while I stab arrows at high velocity into enemies. It's great fun.

Don't forget that the Block perks Power Bash, Deadly Bash, and Disarming Bash also work with bows. Back yourself up with a shield and you'll be able to inrease your skill in blocking and take those perks. By the time you've reached Power Bash, the bow is an effective melee weapon.

Take a look at this build! It seems to fit your wishes, and it even fills the gaps in close-quarters combat you might experience...

http://theskyrimblog.ning.com/group/character-building/forum/topics/character-build-the-demonhunter

That's how i play.

Apparently Power Bash does not work with bows, but Deadly Bash and Disarming Bash do.

http://www.uesp.net/wiki/Skyrim:Block#Skill_Usage
http://www.uesp.net/wiki/Skyrim_talk:Block#Bow_Bashing...

I have not verified either of these for myself. I do use the bow to bash, but I have not taken any Block perks.

Pure archer? Without sneak? It can be done, just don't go up against a group at once. Whittle them down.

Pure archer without sneak, alchemy, enchantment, illusion, conjuration, or any follower? That's just tedious.

Easily doable, really you're just being less effective for the sake of being less effective though.

I suggest you also use Paralyze potions/spells and the slow applied by icespells/-enchantments.

That works.

Also use poisons to add to your DPS, especially if you have a group to deal with. You don't need stealth, just stay well back and maybe close to cover that you can sidestep into and you can remain unseen so you can whittle down the enemy to a more manageable number. You can also use arrows as distractions, if you have not been seen yet, fire one well past them so it hits the back wall and they'll go to investigate the noise which takes them away from you.

Yes and no. To some extent it is meta-gaming to avoid the game becoming too easy. But also the meta-gaming is kinda reasonable. If you shoot a dude with an arrow, is he really going to stop looking around and mutter "just getting jumpy i guess" or "probably nothing"? One option is to pretend that your character is so skillful at hiding that he can always get in a stealth attack, and not the inept enemy AI. Another option is to pretend that the enemy are fairly diligent at looking for you after the initial surprise attack and so you have to take them on in open combat.

this

Legolas would approve of this style.

I would definitely put a lot of perks in alchemy so that you can have one shot lethal poisons. I would also take advantage of frenzy poisons, so that bandit groups could do a lot of the work for you.

Bullseye is detrimental to an archer IMO. It barely offers a benefit, makes the target harder to shoot (I guess this probably isn't an issue for PC players, but I'm unfortunately stuck on xbox for a while), and nine times out of ten makes your shot miss since they become paralysed before the arrow hits them.

This could be a fun build, because archery is overpowered later on when you add in your skill, enchantments, high end equipment, and alchemy. At least playing this way you would not be getting the sneaking bonuses. I really like the idea of allowing only 1 sneak shot per encounter too.

I haven't read all the posts, but bashing with the bow in close combat adds a lot to an archer-build. It's also quite effective, and give you time to run or shoot that final arrow. The enemy staggers quite often in my experience.
Maybe someone knows if bashing with a bow benefits from the shield perk-tree.

Edit: Maybe some have mentioned it, but the paralyze poison is fantastic if you are in real trouble. The only thing is its almost to effective and I tend to use it only when I have died several times in the same battle and have no other options left.