So my favorite place to go in Rochester is LUX. It's located at 666 south ave and two of the bartenders have pit's. In fact one of them technically introduced my significant other and I. His name is Havoc and he's the resident bar dog.
They have a nice backyard too where dogs of all shapes and sizes play during nice weather. I suggest Checking it out with out your dog first to see what's normally there on the night you're thinking about going. Think like you were going to a dog park when deciding if it's a place that you're dog will do well at.
They are big dog lovers, and pit supporters. Great place to support.