I would not hesitate to rent a car, but I would try to make the journey up and down the peninsula by train because the road can be a solid line of traffic at times. While I haven't looked at up-to-date bus timetables, I don't anticipate that they're much better than the last time I was there. IME it's a pain to fit my plans around infrequent, local bus services, and taxis tend to be costly (and sometimes time consuming). Neither bus nor taxi gives flexibility to take detours or stop in isolated spots and enjoy the scenery.

Some people break out in hives at the mention of renting a car in Japan. It's not a discussion that I have the patience for any more. What works for me is not everyone's cup of tea. YMMV, as they say.

If you want to stay at a deluxe hotel property with knives and forks rather than chopsticks in the restaurant, I would check out sites like ikkyu. You can find a few places like this that might tickle your fancy:
http://www.raku-yu.jp/
The pool will certainly be closed in Nov. despite temperatures that I'd feel comfortable swimming in ... I remember being down there in T-shirts and shorts at Christmas one year.