For my next playthrough I want to play a Vampire/Necromancer. I was hoping for some opinions on what kind of build it should be. Conjuration obviously, but should I use light or heavy armor? or just robes?

Also are you not allowed in towns as a vampire?

not sure about armor, if you plan on enchanting then armor will work fine, light or heavy is up to you, heavy offers more protection, but you run slower, but robes work too, at low levels i find robes work better, i personly only use robes on my mage only classes, and vamps can be in any town as long as you keep up with the feeding and keep your vamp level at level 1, if you stop feeding for too long you become a more powerfull vamp but u also will be attacked on site by pritty much everyone, so town will become hostile to you on site, and also if you plan on being a vamp i would also level illusion and restoration, as they will be helpful for staying alive.

I'm playing a pure mage/necromancer vampire right now.

It's worth going into restoration for the necromage perk (restoration 70).

Once this game has enveloped your life and you max out alchemy and enchanting, you only really need one piece of armor. Seriously, you can just put a pair of boots on and you could probably hit the armor cap. Also, invest in Necromage for sweet undead bonuses.

Restoration for Necromage perk. All spells (including enchantments) will have more effect on you, since you count as undead.
Illusion...
Light or Heavy armor, doesn't matter. You can cast in armor at 100% effectiveness -.-
Stage 4 vampires will be attacked on sight, anything before that is fine.

Restoration perks that benefit a vampire are:

• Respite perk restores stamina when you use healing spells, useful since you do not restore stamina in daylight.
  
• Recovery perk allows you to regen magicka during the daylight since you do not regen magicka in daylight either.
  
• Regeneration improves your healing spells by 50% and is the requirement for Necromage perk.
  
• Necromage perk because it makes all enchantments, buffing spells, potions, pretty much any beneficial magical effect 25% more effective for you.
  
• Novice restoration is a prerequisite for everything.

For conjuration perks, all you need if you just wanna be a necro, is novice conjuration, necromancy, dark souls and twin souls. Four perks for max effectiveness!
Necromancy spells are all relatively cheap, Dead Thrall is the best and by far the most expensive spell which will cost 593 magicka if you do not have any conjuration magicka reduction cost gear. But you can carry a light weight enchanted conjuration set for that and most of the time you will raise thralls out of combat.

Now here's the real decision, do you plan on gearing your thralls and enchant and smithing their gear?

If so, you gotta make a choice to go down the light or heavy smithing path.

Now if you are gearing yourself out, heavy path is usually the better choice even if you plan on using light armor, you could go down the heavy side of smithing and get the best daedric weapons and still get the best light dragon scale armor at 100 skill.

But thralls on the otherhand, will get much better benefits from the light armor smithing path.

Here are the reasons why:

• The best non-unique thralls, Volkihar vampires, best armor is glass, which is light.
  
• The most common armors for light armor using thrall candidates will be hide, leather, and scale.
  
• The most common heavy armors are iron, steel, and plate which are also on the light armor side.

If you don't care about thrall survivability and want the best damage for weapon wielders, then go heavy. But glass weapons aren't really that much worse than daedric at high levels, and thralls don't get reduced damage on higher difficulty levels, players do.

If you plan on using Vampire thralls or Magic users, then the light smithing path is definitely the way to go, since your thralls will rarely use weapons anyway and since you do light smithing, then use light armor.

I'm just mentioning this since on my necromancer I used to go down both paths for smithing to improve thrall gear, and I noticed that 99% of thrall armor is on the light smithing path.