163 is relatively straight and flat. There's a bit of a grade, and corner, at Mexican Hat where it crosses the San Juan river. And a bit of grade further on where it crosses a ridgeback.
The visitor center for the Tribal Park is about 4 miles off of 163. That and part of the parking is paved. The road through the park is packed dirt, most suitable for a car. You can look at the road in detail with Google Maps Sat view, and selected Streetviews.
I don't know if there's good upto date information on what it costs to visit the park, drive the road and/or camp there.
North of Mexican Hat are other sights. Others have mentioned Goose Necks, a Utah state park. Just beyond that is Moki Dugway, a grave switch back road up a bluff, and Muley Pt overview at the top. At the bottom of the Dugway is a road through Valley of Gods. That too is gravel/dirt.