A few suggestions. I don't know about tours because I've never done those.
1. Iceland. Cool viking history, absolutely epic hiking and scenery, hot springs, sometimes swimming if it warms up (I went swimming in the ocean at about 12 degrees C, but nobody else did). A lot of people like to rent campervans and really explore. Restaurants are expensive (and nothing to really write home about), groceries are normal priced.
2. Japan. This would be my top choice given your criteria. The cultural side of things in incredible, with all the temples and castles and museums. The hikes we did were unreal, especially because they tended to line up nicely with gorgeous onsens at the end for a nice soak. The fast train network makes it really easy to see as much of the country as you want. We loved the food as well, though restaurants were at the higher price range and accommodations were less likely to be set up for cooking.
Those are the expensive ones. Now, two cheapo ones that I liked just as much.
3. Guatemala. It's a real gem, mostly undiscovered by tourists. Everything is very cheap - accommodations, food, tours. The hiking is incredibly epic and involves volcanoes and lava (I literally went there because I wanted to climb a volcano). You can have all sorts of cool experiences that don't exist elsewhere. The historical stuff is cool too, like the palace, Mayan ruins, Spanish colonial architecture, etc.
4. Thailand. So much awesome cultural stuff - museums, food, temples, etc. Tons of amazing nature stuff and hiking - we did a group hike through the jungle followed by some river rafting, and another day hiked up a gorgeous seven-tier waterfall with swimming at each level (and some sort of carnivorous fish, but the scenery is worth the bites). Everything is dirt cheap once you're there. The food was some of the best we've ever had anywhere in the world.
