Oneonta in August is hard. When would you be looking? A weekday? Weekend? Early or late in the month?
The big thing with the area in August is the baseball camps are still going on, tourist season is still in bloom and the colleges start coming back. Many of the hotels on a weekend will require two nights stay.
The Red Carpet Inn on the Lake. I have never stayed there, but I have heard pretty good things about it. It always seems busy and it's in a very nice spot. Depending on your plans, you could always do one night in the Oneonta area for when you go to Cooperstown and possibly stay in the Cobleskill area when you are at Howes Caves. There is a Holiday Inn Express close to Howes Caves.
The chain hotels in Oneonta are decent, too. As is the Rainbow Inn in Oneonta. That one, too, is close to Brooks' BBQ, which is a wonderful place to eat and is very well known.
Prices in August will likely be up a little bit, too.
While at Howes Cave, if you are looking for a double-dosage of caves, Secret Caverns is also up there and Secret Caverns features a 100-foot underground waterfall.
I second the recommendation for Secret Caverns!