East 3rd is pretty cool ( i think thats where Lola, Greenhouse, Saigon are) across from the Q. Although its a bit further from the rock, across the street from the west side market has some great places. Great lakes' pub is a stand out for me there
I would say E. 4th is a good place, also W. 6th. If you look towards the burbs more, it depends on how much you want to spend, but there are some nice places in the area. I like Fire in Shaker Square. A little pricey but very good food.
Tremont and that proximate area is good. The Taphouse on Scranton has an excellent beer selection and good food. There are many good restaurants in Tremont as well: Lolita, Parallax, Sokowlowski's University Inn (if you like family style); and for late drinks a good place is the Velvet Tango Room a retro martini bar.