They are on opposite corners of Abbott Road and 20A. Danny's is bigger and more upscale with a restaurant. The Big Tree Inn is more of a little corner pub atmosphere and the wings are slightly better. You could easily do both, they are about a 150 yards away from each other. And no, I'm not converting it to meters.
I wouldn't recommend staying at the Hyatt downtown unless you have some downtown activities. Where you stay will depend on what other things you plan to do. PM me if you want.
When I go up for the opener, I'm staying at the Hampton Inn in East Aurora for the 1st two nights. It's a small property and the village of East Aurora is beautiful. Quaint shops, narrow streets, big trees etc.
Then Saturday night and Sunday night will be at the Holiday Inn Hamburg because it's closer to the stadium.