I’m both a parent and an alum so have stayed at a LOT of places in the area. As far as hotels go, we have stayed at The Kenyon Inn (which should be more available in summer), Mount Vernon Grand, Mount Vernon Inn and Holiday Inn Express. MVG was a little nicer than the others, but we usuallly stayed at MVI because it was often less expensive, and they had a nice breakfast included in the morning, where we could bring our student for a small cost. I also stayed at HIE a few times and it was often perfectly fine, though the rooms/experience tended to be a bit more hit or miss. When more friends or family are there, we usually stayed at Airbnbs. I have found reviews on the site to be generally accurate, but feel free to reach out if you would like specific recs.
Gambier is obviously most convenient, but Mount Vernon is easy to get to, near most of the shops and restaurants in the area. Howard is another option for both food and lodging, about 10 minutes east of Gambier, but that makes it farther from Mount Vernon.