Park ave might be your best bet. lots of good restaurants, non-chain shopping places, and there is a park ave crossfit gym.
http://www.park-avenue.org/park-ave-summer-art-fest.html (close to east ave wegmans, mentioned below)
South wedge is something to look into. lots of awesome places in south wedge.
http://www.southwedge.com/ tap and mallet is my favorite bar. 50+ craft beers on tap.
corn hill has some nice brand new apartments with some cool festivals
http://cornhillartsfestival.com/
http://www.rochesterevents.com/ lilac festival is cool too. this is in between highland hospital and strong. some people do some of their residency stuff there i think.
Hennrietta is outside of the city to the south. Places are sort of walkable to each other but it has everything you want. Gym, lots of restaurants, a mall. This is right by RIT campus so you could get a membership to that gym (pricier but very nice - pool, raquetball, tennis, soccer, classes, full gym). this would be a 10-15 min drive to your job.
Oh and if youre not familiar with Wegmans, there is one on east ave that you must check out. best grocery store ever IMO. there is one of those in hennrietta too. the one in east ave is brand new with it's own wine bar in it.
Places to check out:
Wegmans (multiple locations)
Drinking: Tap and mallett, dragonflys, half pint, genessee brew house (good food too), lux (if youre part hipster like me), Roc brewing co (used to live by them, great friends of mine)
Food: dinosaur bbq, open face sandwiches, everything on park ave, dibellas subs (hennrietta), owl house (hipster), NAPA pizza (extremely fancy pizza w/ own beers)
strong national museum of play (the kid in you, home of toy hall of fame and interactive stuff), little theatre (old movies in landmark), george eastman house (museum)
sports: rochester red wings (baseball), rochester amerks (hockey), rochester rhinos (soccer), RIT has a good D1 hockey team
If I were in your shoes. I would look to #1 park ave, #2 hennrietta. if youre more a city person, park ave/south wedge for sure.