I lived in parktown place. I think I paid like $1300 for a 1br, but 2br were only like 2k iirc, so would be under your budget if you had a roommate. Apartments were very reasonably sized ~750sqft for a 1br. Each floor had washers/driers.
The complex of 4 buildings had its own small supermarket, drycleaners, decent gym, swimming pool etc. About a 10m walk from downtown. Each building has doorman etc. On ben franklin parkway so get a nice view of art museum, plus it doesnt feel as city like even though you are so central.
We looked at a bunch of places, and it was by the far the best bang for buck combo close to center city. A lot of the places we looked at that were actually downtown were like $1600+, and were not any nicer.
The places werent super baller or amazing, but definitely as close to as good as you can get for that amount of money in that location.
Decent talent at the pool as well sometimes