My $0.02:

1. Your requirement for "thin wheels"? It isn't the width of the tire that works against you (especially for a ~2 mile trip), but the amount of tread on the tires. Smooth, wide(r) tires lend themselves to an urban commute rather nicely

2. From a monetary standpoint, you might just be better off renting. You won't recoup your initial investment if you buy new and trying to sell it after the Summer is over is not the best time to be selling either, as demand goes down for bikes as the temps drop.

3. Honestly, unless you have serious time constraints, consider walking.