Yeah, the only thing is there aren't any free unowned beds in the college.
Yes there is. In the Hall of... I forget the name, but when you join the college you're given a dorm-room type of bed where the other students live. I think it's the first bedroom on the right as you enter. Obviously, if you become Arch-Mage you get the AM quarters with its own alchemy and enchanting tables. But it's a hassle to live in and if you decide to marry, you can't move your spouse there (lame).
The next two options are Honeyside in Riften and Vindrel Hall in Markarth. Honeyside is easily the more efficient of the two but nowhere near as cool as Vindrel. But neither place is ideal for the character decribed by the OP.
I personally hate Hjerim. It's the most ineffiicient of all the homes. Proudspire is nice but from level 4 it's going to take some time to save up the coin to buy it (plus the upgrades---total around 38K).