I can only speak for the Redwoods…
There are some nice Redwood trees South of Jedediah Smith, and you are right, that is a looooooong drive from the bay area (SF).
There are some ok trees further South, say, Humboldt Redwoods State Park, but if you are going to drive all this way, you should really spend your day or two here at Prairie Creek Redwoods State Park. The campground can be kinda expensive (35 bucks last time I was there) if you need to stay at a campground for a night (hot showers are there too). The truly perfect hike would be to depart from the visitor center at PCRSP and hike the Miners Ridge and James Irvine loop… which is about 11 miles. However, half way through it is a beach campground that you can tent camp at called Gold Bluffs Beach Campground. This is a really special spot because there are a herd of rossevelt elk that live on this beach (maybe 1 or 2 miles in length, so while not guaranteed to see them, chances are pretty good). It is also really special because it is where “Fern Canyon” is located at… and it is one of those magical things that when the sun comes up early in the morning and you are inside of the canyon, it is, well, just really special.
What you could do is: hike in on the Miners Ridge Trail (~6 miles IIRC) to the beach camp ground and call it a night. The next morning pack up and experience Fern Canyon in the morning, than there is an unmarked (but very easy to find) trail that will take you North along the canyon wall and the beach. It is ~4 miles (IIRC) up to the the northern most part of the beach. Along the way you will get to hike and see all these cool things. Once you get to the Northern End there will be a huge pile of rocks around this really neat freshwater pond with all kinds of birds. There is a now-closed campground that still has a bench so you can setup there and have some lunch. Than hike back down to Fern Canyon and take the James Irvine trail back up to the PCRSP. Jump in the hot shower, jump in your car, and have a huge smile on your face knowing you have just hiked through some of the finest Redwoods that exist on the planet.
There are also a few other small trails around this spot that you could do to fill up half a day.
On your way up to here you could also bounce off highway 101 just South of Eureka, drive in about 10 or so miles and hike the ~11 mile Elk River Trail, also known as the Headwater Forest Trail… also known as the place where Julia “Butterfly” Hill spent 700 odd days camped out in the top of a Redwood tree to save it. It was the pinnacle of the battle between the timber companies and the environmentalists, back in the late 90s, and which brought about the end of most old growth timber cutting throughout the entire Redwoods of Northern California.
You could, of course, also spend 2 days hiking part of the Lost Coast Trail – which is of course one of the top hikes in the country. It is about 4.7 miles down to Spanish Ridge/flats which has a nice off-beach camp site. Trust me when I say that while it is only ~5 miles, it will feel like ten miles. It makes for a wonderful overnighter and could be a way to spend an extra 2 days up here. You will not see any Redwood trees on the trail, it is all about hiking the longest stretch of non-developed beach in the CONUSA.
Lets see… there are a bunch of other really beautiful day hikes up here, but for the best of the best of the Redwoods, that kind of lists them all, at least the ones that are overnights and worth seeing.
(edited reason: omg… spell check john!!!)