2-day trip from San Francisco in early May & rental car pick up

Others may be able to answer some of your questions, however, one site with huge trees not far north of San Francisco is Muir Woods - note, you would need to reserve parking/shuttle bus. Amazing area for nature walks! We have driven there on day trips while staying in the city.

https://www.nps.gov/muwo/planyourvisit/index.htm

Muir Woods is a wonderful place to see redwoods, and there is a lot of hiking in the area. Rather than driving all the way to Humboldt, you might look into Bodega Bay and the surrounding area. Depending on when you are there, you should be able to find lodging in your price range, and it is a good spot to use to explore the California coast further.

Thanks. I have been reading some guide books, and I think you are correct that Bodega bay may be the ticket. There are some cottages near Occidental in second growth redwood forests. Bodega Bay is close and is also a birder's paradise; by the look of it. I believe I can get to Muir Woods as a day trip from San Francisco. A shuttle from the ferry terminal. Maybe I can figure out the rental car from there after visiting the Park. I'll just pack a light backpack for 2 nights.

I lived in San Mateo for a few years. When I go back to visit, I fly into SFO and then get a car at one of the local offices in South San Francisco or Burlingame - a few minutes' by taxi or BART (depending on which one you choose) and get a better price, mostly because of the steep airport surcharge.

Traffic in the city isn't so bad, but driving into and out of can be miserable because of all the commuters - many of whom are going to or through Sausilito.

If it were me, I'd take BART as close as possible to the friend for 2-3 nights, then get a car in the city and drive north for 2 nights, then back to the city to drop the car and spend last nights with the friend. Take public transportation to Muir Woods (parking can be miserable). You could just meander along the coast road maybe as far as Mendocino. The Avenue of the Giants is an amazing drive through old redwoods but it's a long way to go but if you have 2 nights, and spend at least one of them in Mendocino, it's worth it.

I grew up in that area and am actually doing something similar to you in a couple of weeks.
I'm renting a car at SFO and driving up to Sonoma County. I'll visit the giant redwood grove called Armstrong Grove in Guerneville (much less crowded than Muir Woods but equally impressive!), and then head up to Sea Ranch on the Sonoma Coast. Sea Ranch is a great part of the coast with sweeping views of the sea, meadows, redwoods all around, and small villages with great food and people, deserted beaches, and walking trails. Takes about 2.5 hours to get to Sea Ranch from SFO. You can rent a house, which is what I'm doing, or stay at their lodge.
That area is my idea of heaven.
$150 per night is not much for the Bay Area or Sonoma County. If you wanted to stay in Guerneville or one of the small towns up highway 1 from there, up along the coast, you may find somewhere for that price. Some of the towns are Gualala, Timber Cove, Annapolis (really up in the trees!), or Point Arena. All are beautiful and surrounded by the nature you are looking for.
Humbolt is about a 6-7 hour drive from San Francisco and not worth it for just two nights...beautiful but you need at least a week to do that area justice!

Chani and Anita, thanks for the additional suggestions. As I arrive on a Friday, I didn't want to head north on the weekend. So renting a car at SFO wasn't on my mind. However, if I can drop at the airport after picking up elsewhere, that might solve some transport issues or give me a bit more time to add to this part of the trip.
Google was saying 4 hours to Humboldt State Park, so I appreciate the more realistic time frame. I guess it is out.
I think the recommendations for Sonoma Coast or inland would be enough for a short trip without spending all the time on the road.

Thanks again.

Lived in Sonoma County for 16 years. Ditto suggestion for Armstrong woods over Muir Woods.

Are you into wine and visiting a couple wineries? If so, can give you a couple suggestions.

We’ve done the below route of various with many visiting friends or family.
Drive from Santa Rosa on River Road toward coast. Stop at Armstrong woods then to Jenner. There are beaches there to visit. You could drive north on Hyway 1 to Fort Ross (where Russians occupied California for a short while). Then head back south on Hwy 1 to Bodega Bay. Doran Beach can be a nice walk. Then head inland again to Sebastopol,, or if you are up for more coastal driving, continue south on 1 to Point Arena.

Very different and undeveloped, unlike Monterey Coast.

Karen, thanks for the other info. I do like wine, but hadn't planned on visiting them, only due to time and wanting to be a responsible driver. But I guess it wouldn't hurt to have recommendations of a few for purchase considerations.
I do have Fort Ross on my list, having learned about the Russian fort back when living in Monterey. So, that area is looking more and more like the place to be.
I have been having problems getting notifications from my airline, and a recent check to my account shows they have changed my flights to arriving a day later than planned. If that is the case, this trip might need to be nixed. I'll see if I can get it back to what I originally booked.
Thanks again.