Some of our tourist attractions have shut down in some respects due to new events and decentralization, but there there other interesting things to do and places to check out still, and we're getting new things to do and places to see as well as more people move in. There is a new golf course for instance that is being opened by a fellow mover. I doubt anything else will be happening specifically on Sunday afternoon- but we do have events that conflict with each other pretty frequently. There are more things going on here than one has time for let alone can go to given conflicts of events.
More realistically some interesting places to check out in Keene on Sunday afternoon probably include places like 101 Local Goods. It feels to me like a touristy kinda place, but apparently it is very popular with the locals. My love affair with it is that they take Bitcoins and other crypto currencies. There is also a Bitcoin vending machine at this business.
Another place nearby I'd recommend going is Kirby's Q in Alstead. While most people like the BBQ (as do I, but...) I'm obsessed with the home made sweet butter. I'm trying to get the owner to start selling it at 101 Local Goods in Keene. Alstead isn't in Keene, but is nearby. Probably about a 20 minute drive from Keene. It's a great little spot and they take Bitcoins as well.
Another place that some of us like to go for lunch in Keene is Pizza Down Under. The owner might start taking Bitcoin at some point here too. He came off to me as being quite interested in learning more about it not that long ago. The main stumbler in many cases is owners finding the time to add the payment option. In any event it may be a good place to meet you at if you want to get some lunch on Sunday.