Welcome to Cbus! I echo Buffalo Bud on Thurman and Mohawk. Thurman is usually like a 2 hour wait for a table though. There is a lot of good stuff in the Short North but it will be real busy down there since it's pride week. Very "artsy" scene in that area. I like short north pint house for beer and upscale bar food.
The Easton area and Polaris area up north will have all your typical shopping and "chain" options. I'd stick to the arena district /short north/ German village areas for some more "local" vibe.
I'll throw out 2 more random suggestions for food. Lindys in German village is fantastic and has a great outdoor patio. Had our rehearsal dinner for our wedding there. Also if for some reason you're interested in a steak, The Top Steakhouse in Bexley. It's about 2 minutes from my house and is a total old school steakhouse that looks like you'd expect the rat pack to hang out in. Dark, piano player, stiff drinks, simple menu, etc.
Hope you enjoy Cbus happy to answer any more questions!
Oh and if you're looking for something a little different, check out 16 bit (bar / arcade) or pins mechanical co. (Pinball /bar/ duck pin bowling) Also lots of good local breweries: four string, hoof hearted, seventh son to name a few.