you can also hire a car and driver to take you places for day trips and beyond. That's still relatively inexpensive and worry-free. I wouldn't ever want to drive a car there myself either. But I don't even like driving at home.
There are lots of nice national parks. I would contact a local travel agent and see what they can put together for you. Thailand has lots of nice things to see away from the big city. Many years ago I did a nice little itinerary that went to Khorat and visited places like Phimai, Phnom Rung and some other Isaan sights. I had a guide and driver/vehicle. Most of my travel around the region was done that way. As a solo traveler I always liked having somebody deal with interpreting for me and showing me around.
I agree that Sukhothai is a nice place to visit. I did that as a similar multiday trip that stopped in Phitsanulok and we also visited a national park that had some nice hikes.
Lopburi is also doable as a day trip.