If you want to stay by the National Baseball Hall of Fame and Museum, you can't get any closer than the Baseball Town Motel. The Baseball Town is just a couple of doors down from the HoF, and is right above one of the memorabilia stores (in fact, registration is at the counter of the store).
The owners of the store/motel are fine people and very friendly. I have stayed here twice (both times in 2001, February and for the Induction Weekend) and the owner told me as I checked in for the second time there that she would put me in the same room I had when I'd stayed the first time.
The rooms (or at least my room, number 6 I think it is) are dark, small and slightly shabby, but still clean. The rooms all have color TV, but I forget the extent of the channels. I remember local stations from Utica and Oneonta, as well as ESPN. Each room has an air conditioner, but otherwise the rooms are no-frills. light-weight towels and perhaps the smallest bar of soap I've ever seen. Like most motels, there is a vending machine on property.
The side-benefit "frill" is location. You are on Main Street, and not only close to the HoF, but pretty much everything one would want to see is on this one drag. The motel also has free parking for its guests, and during the summer, you can't ask for a better perk. The parking is out back, with a staircase leading right to the lot. This is the secondary entrance to the motel, with another entrance on Main Street itself.
The prices vary depending on the season. Cooperstown is very slow in the winter months, and some places reduce their hours drasticly. The price at the Baseball Town Motel reflect this. My winter stay was about $60 bucks a night while the summer weekend rate was up over $100.
For a small town, Cooperstown has a large number of accomodations. What sets the Baseball Town aside from the other places I've stayed at are the location and hospitality of the owners. I'd call this is the low-end of the accomodations in Cooperstown, but if that's so, low-end here is middle-end compared to other places I've been.