BarryG is right on almost all counts, except that there are a couple of high rises right on Washington Square-- both are condo buildings, but likely have several units that are on rent at any given moment. Independence Place and Hopkinson House-- would be ridiculously close to Curtis Center-- just across from Washington Square! And in fact, Independence Place is two large (twin?) towers. Studios in either of those likely go closer to $1000 or more, however. I live in one of these buildings, and I rent, so I know.
Generally, however, rentals in Society Hill and Rittenhouse Square areas aren't going to be that cheap, that too in the high rises. And overall, due to Center City's lack of vacancies and the housing market the way it is, rental rates have been creeping up and the vacancies are very low. So it's the landlord's market.
And for me, a trip to Trader Joe's is easy even without a car (I gave up my car when I moved here from Dallas, TX)... if you have to, you can take any of the buses going west on Walnut, then just walk a few blocks north to 21st and Market to Trader Joe's. Then on the way back, even with grocery stores in hand, just walk two blocks south to Chesnut St, and take any of the buses back east to your nearest stop. Sure, the arm muscles can get some nice toning if you're not careful with what all you're putting in the grocery cart...but it's doable. I am a guy, so I guess it's easier, but I'm not particularly muscular or anything.
"The only difference between the Republican and Democratic parties is the velocities with which their knees hit the floor when corporations knock on their door. That's the only difference."
- Ralph Nader