Though there are not too many of them, Red Lion also accepts pets and if you join the Red Carpet Club they waive the pet fee when you stay. I stay there when I go to shows up near Eureka where there is not La Quinta.
The Red Lion in Eureka must have a steady stream of Basenji owners passing through, we spent the night there with the dogs just a few weeks ago on our way back from San Francisco.
In San Francisco itself we stayed at Hotel Triton - they have an open-door pet policy with no restrictions on breed, size, number or type of pets. We just gave the hotel the names of our Basenjis and our room was set up with a pair of huge dog beds, two bowls per dog (one full of kibble!), bottled water, and dog treats. Plus, they welcomed the dogs with a sign that remained up all week (and yes, that jar on the left of the photo does contain dog biscuits.) and were more than happy to empty out the minibar so we could store the raw food in there. The paperwork in the room also had lists of local doggie day cares too (which we didn't need as my employer's office building permitted dogs.)
The Triton is part of the Kimpton hotel chain, each of them has a similar pet policy. Their rates aren't the cheapest but there's no pet deposit (just a waiver you sign at check-in). I think that for the sheer convenience and for the way the dogs were treated it was well worth it.
What holds me back from traveling is that I don't want to put the dogs in the cargo hold of an aeroplane, and I can't drive everywhere (we have family on the east coast, and that's a very, very long drive.) I'd love to travel by rail, but Amtrak forbids non-service dogs on board (interestingly, where I grew up, they don't care about dogs on trains as long as they don't take up a seat.)