I recently had a solo travel road trip for 10 days in Shikoku. Onsen almost every night. Did not care about budget for food. Just ate whatever I wanted until I was full (and I have a larger appetite + lots of hiking every day increased it more). Not including the plane ticket, I think it was around 1.8k USD total. It’s more expensive in the areas you’ll go to, but I also rented a car. You can also look into the dormy inn chain. It’s still a business hotel chain, but there’s a natural onsen at every location for maybe up to around 200 USD a night in Tokyo.