Crater lake is mostly about views of the lake. There are a couple trails around the rim for that. The Discovery Point trail runs along the east rim, is relatively flat, and has a lot of access points just off the main road there. The Garfield Peak trail climbs up to a higher peak on the rim and has what I think are the best views. It's 3.5 miles round trip from the visitor center. The only access to the lake is Cleetwood Cove trail on the northeast rim. It's a mile long but is crazy steep. Keep in mind that the rim is over 8000ft elevation and there will still be a good bit of snow. Some roads and trails might not even be open until late July.

The best areas in the redwoods are in the state parks. The national park was established much later and is mostly there to protect the watershed. I recommend seeing Fern Canyon. There's a 9 mile round trip on the James Irvine trail from the Prairie Creek visitor center that's pretty scenic, or drive to the fern canyon parking lot and it's only a mile walk. There are a lot of trails in Del Notre and Jedediah Smith state parks, but they are poorly marked. Your best bet there is to talk to a ranger about what you're looking for.

Safety tip - that area has a lot of elk who like to hang out in the road. The roads are curvy and it's pretty common to come around a blind turn and suddenly be face to face with a whole herd of elk. So drive safe and be prepared to stop quick.