We make this trip quite often, as I grew up in California (San Diego and college in Long Beach).
We always book using rentalcars.com - We usually are planing well enough in advance that we book about 10-11 months out, and then have the ability to monitor the pricing. Most of the time we are paying less than half what the car companies are charging. All of the insurances are included, except maybe personal injury (for yourself, which your travel insurance would cover). At the counter, they even say "you are fully covered so no need to pay for insurance" as opposed to the usual up-sell. We did a one way rental, and had no return fee from San Diego, a lot of the companies need to get cars BACK to LAX. The worst we've paid is $100.
As for where to stay, is there any reason you don't want to just go from A to B to C and stay along the way, as opposed to going back to base each time. California rush hour is practically all day... Despite having to pack up each morning, it might be more relaxing than driving back for 1-2 hours after a day of sightseeing.
If staying in San Diego, I always try to stay somewhere within walking distance of the
Old Town Trolly . It is a great way to get around to the touristy areas, and not have to drive, park, etc. Usually we are meeting up with friends at places along the route anyway.
If you go out to Mission Valley, you might find lower hotel rates than downtown San Diego.
Going north, if you like wine, consider Temecula, they have some lovely wineries around, and you can find some decent hotels (My parents are grey nomads based out of an RV resort about 20 minutes from Temecula, so we stay there when we visit).
If you want to avoid LAX, but still be in the general area, Marina Del Rey is a nice area and close to LAX. We usually stay in West Hollywood of Beverly Hills though, as we usually only go to LA for dining or shopping.
Another consideration is fly to Seattle from HNL and drive down the coast. 10 days is a bit quick, but you could see some great spots like Sequoia National Park, Portland, Napa, San Francisco, Santa Barbara, San Diego.
San Diego Tours by Old Town Trolley | San Diego Sightseeing Trolley