Unless I win the lottery, it's all about the trade-offs. I'll take these.

Preferred:
√ Classical style, no 1970's look!
√ 750+ SQFT for a 1 BR, 1100+ SQFT for a 2 BR
√ Good walkscore, lots of businesses nearby
√ Available light, lots and lots of windows
Open space layout
√ Good bones, not much large-scale change needed, but sugar-coating inconsequential
√ Good neighbors and surrounding area
√ Bargainish. I can't stand paying full price.
? Energy Efficient (I suppose I'll find out)
Close to public transportation
<> Not too far from downtown, wherever that happens to be (close enough)
Hardwood, polished concrete, or tile floors (carpets will be removed)
Not central air if possible

Bonuses:
√ 950+ SQFT for a 1 BR, 1350+ SQFT for a 2 BR
Fireplace
Skylight
Granite-ish countertops
Radiant Floor Heat!
√ Basement
√ Parking included
Water softener, no hard water stains
√ Deck

Unimportant:
√ Garden space
√ lawn