If you head into Syracuse, there is Middle Ages Brewing Company, which is pretty good, some of their styles are a little hoppy but still pretty good. Their Grail Ale is really good! You should be able to find some of their beer around the upstate area in grocery stores.
Another beer that you can find around the area in stores would be Sackets Harbor Brewing. Check out the 1812 Ale (its a copper color pale ale - not tooo hoppy though), it is one of my favorite brews! They also make a pale ale I hear is good. Wagner at seneca lake also makes the Landmark Brewing Company beers. Landmark beers are not that good. Wagner brews didn't impress me either, honestly.
Lake Placid Brewing is a bit north of the Upstate region, but their Ubu Ale is really good if you like a nice strong brown ale. Grocery stores carry it as well. I've already seen Ommengang posted on here. There is also Cooperstown brewing company. If you head to Buffalo, which 2 - 2.5 hrs away, there is Pear Street Brewery - A must try!!!, and Ellicottville Brewing. Rochester is ~ 1 hr away and they have High Falls Brewing (Genesee Brand and J.W. Dundee) and Rohrbach.
Hope this helps!