Eureka is a popular place to stay when exploring the redwoods. It's the biggest "city" in that part of California and has a lot of lodging options, including nice B&Bs, chain motels like Best Western, and lots of things to see and do especially around the Historic district. However, it's still about a 45 minutes drive south of the Redwoods National and State Parks. We enjoyed our stay there when we visited the redwoods last year. I've also heard that Arcata, which is just north of Eureka, is also nice. It's a college town (home to Humboldt State University), and also has a variety of lodging and dining.
On our way north from Eureka, we passed by Trinidad, which has a beautiful light house overlooking a quaint cove and feels almost like it belongs in New England. There are a number of B&B options there, and we'd consider staying there next time. Lodging is obviously pricier than motel options, but apparently fills up fast.
While there's a lot of beauty at the Redwoods National and State Parks, locals we met in Eureka actually recommended we check out Humboldt Redwoods State Park where they said there are taller trees. This is about 45 minutes south of Eureka, and you can turn off of US 101 onto the Avenue of the Giants to start exploring. It was well worth a detour on our way back down to San Francisco.