A couple of restaurant suggestions:
Pasta Villa on E. Ridge Rd. Expect a wait, but they have a bar. Real nice Italian joint. On the outskirts of the "city", but Rochester is a small city and generally easy to get around (though if you are coming from downtown, I strongly recommend taking I490E to I590N to NY104W, get off at Portland. GPS may try to route you through surface streets from downtown, not advised.)
Beale Street Cafe on South Avenue. I'm not a huge fan, but it's OK. The primary reason for the rec is you may find yourself at the German House that same night. Even so...
Tap & Mallet on Gregory St. is better. High end bar food, good tap selection.
India House on S. Clinton for Indian. The inside is getting a bit rundown, but overall always a good meal.
This next place is one of those places that is easily overlooked from the rather small and shabby interior, but Ming's Noodles on S. Clinton still makes great food. Do not let the inside fool you.
As mentioned, local specialty is the Garbage Plate (t) and its variants. It is an acquired taste. However, white hot dogs (not bratwurst) and hot sauce (not hot sauce like tabasco) are also a local specialty. These can be a bit easier to tolerate, and there are plenty of stands around, everyone has their favorite. Just ask at your hotel if you're feeling adventurous.
Live music - check the schedule at Water Street Music Hall (downtown) and German House (Gregory St), these are the larger small venues. Also, Freetime Magazine, www.freetime.com, will have most of the local listings, as will www.rochestercitynewspaper.com.
Now, the "from left field" recommendation for out of town visitors... Wegman's Supermarket in Pittsford. Seriously. And FTR, this isn't my personal oddity, it's actually won (repeatedly) City Newspaper's readers choice award for best place to take out of town guests. I can't tell you why a supermarket is a great tourist destination, but I can tell you that everyone I convinced to visit one (we used to do a lot of training for out of town visitors in Canandaigua) was happy they went. It will also serve as a restaurant recommendation...
I like Canandaigua, I've worked in Canadiagua, we go to Canandaigua, but for a short visit to Rochester, especially if you're cutting out for a day to Niagara Falls, you could probably skip Canandaigua.
HTH