What I mean by this is what house is closest to the shops and a forge and stuff and still can have an alchemy/enchanting table. That means Whiterun is out.

Any ideas?

Honeyside in Riften. Shortest walk to traders compared to other houses.

Yup.

Plus it's handy if your a vampire since it has a second entrance that's actually outside the city walls.

Aye, Riften is pretty comprehensive. You also have your own door out of the city (great for stealth), a skinning rack, a garden and re-stocking fish barrels. One thing that I oddly really miss in Riften is the Apothecary satchel next to the Alchemy table that you get in Whiterun. The lower floor in Riften doesn't have enough practical storage next to the two work areas.

Plus it has that empty room downstairs, unless that's just me. I've only bought and upgraded it on one character.

Sounds like you have the Thane bug? If you become Thane of Riften the empty room is your Housecarl's bedroom and has 3 storage areas. Not that she ever goes down there...

No smelter in Riften is really annoying if you use Smithing. Having to nip up to Shor's Stone is a pain.
Since you've ruled out Breezehome which I find the most convenient I'd say Hjerim is pretty good.

That's right, but usually mines have a smelter near the entrance where you can sort your business out on the spot.

Not the thane, I got the house during the Civil war. That may be it.

But it is odd that the housecarls never go into their rooms, they just sit there eating bread. I'm not sure how they keep in shape. They should release a workout DVD

If you are on PC, there's quite a number of Mods that address this. On places an enchanting station on the table next to the alchemy workbench in Whiterun, which is pretty optimal (especially if you delete some furniture to make that room easier to reach). I like those a lot.
Other's give you entirely new find able / purchasable homes. There's even one that puts a "batcave" in the basemant of any house you buy- and all the houses are connected to that same room! So far I haven't tried any of those.

Well, since there's no smelter in Riften, I'm suggesting Vlindrel Hall in Markarth. It's not that far from the forge down near the waterfall, just run down the stairs and you have the general goods store and a bit further up, the blacksmith forge. But it doesn't exactly have a tanning rack.

Unfortunately I heard of a glitch some time ago where the steward up in the keep glitches, preventing many players from being able to purchase Vlindrel Hall, so next I'd recommend Hjerim. My Hjerim has quite a few glitches, such as none of the weapon racks working etc. It's fairly close to the forge in the market, but i can't say for the general goods store. It's quite far away, Sadri's Used Wares.

There are 2 stalls in the market that sell general goods though.

Personally I like Breezeholm. Has the satchel on the Alchemy lab, it's next door to a forge and smelter. Just down the road from a general store. I do hate the whole no Arcane Enchanter crap tho.