I haven't explored much in that area, but spent some time in Lassen NP when I was a kid. Really cool area with good hiking, fishing, etc. There's some decent sized lakes where you could take the kayaks out. There's also some good trails nearby - High Lakes, Cleghorn Bar, Peligreen Jeepway. High Lakes would be a cool place to settle in for a couple days and explore.
The north coast is gorgeous but not much wheeling. But if you've never driven that section of Hwy 1 it can be fun. Shasta is more for powerboats and houseboats, but there's probably some really cool hiking trails. Surprisingly, I've never spent any time up there.
Sounds like a fun trip. If you want another H3 to run any trails with let me know.