Ok, first bit of advice, call it Western NY to the locals, not upstate
In Buffalo, the place to party is Chippewa St and Franklin st. It is downtown. Chippewa is nothing but bars. Franklin has some cool places too such as the Buckin Buffalo Saloon and D'Arcy McGees. The bars range from dive bars to themes and trendy clubs. If you pick up a copy of Artvoice (free on street corners) you can find out what clubs will have live music (ranges from folk and blues to metal and alternative).
To eat, I would definitely stop by the
Anchor Bar on Main St. It is the place that invented "Buffalo" wings. Another popular local food is Beef on Weck.
Charlie the Butcher is best for that. You may also want to hit the elmwood strip for the college scene. More bars and some unique local shops.
There are more places to eat and places to shop if go outside of the city. Many more people live in the suburbs and the city itself is dying. The most popular suburb is Amherst (voted safest place in America 3 years in a row). The major roads to find stuff there are Niagara Falls Blvd and Transit Road.
Also, you should probably head up to north to Niagara falls (20min drive). The American side doesnt have much (it is decline), but there is a new casino there. If you decide to cross the border make sure you bring a birth certificate or passport.
On the canadian side there are tons to do. More casinos, clifton hill has wax museums, clubs, putt putt, tons of entertainment options. You can also visit the Canadian Ballet. Those are strip clubs that are a lot more lose with the rules, more wild than what you find here. If you need info on proper ettiquette there, PM me.
For Rochester: stop by the Dinosaur BBQ.. best BBQ you'll find in the northeat (imho).. it's a bluesy biker joint.
I"m sure SatelliteGal will respond too with some ideas.