I can't think of anything I personally find appealing in between Sequoia and San Francisco. There are motel and cabin accomodations in Three Rivers, which is the closest place to the park. It's still at least 1.5 hours into the park from there. Wuksachi Lodge, in the park, is the best place to stay.
Visalia has chain hotels and would be the next closest place to stay. Exeter, a sort of suburb of Visalia, would be a bit closer. Neither has any sort of real tourist infrastructure or attraction. It is by far better to stay in the park if at all possible.
It's about 5.5 hours from Los Angeles to Sequoia. If you left in the morning from L.A., you'd be in Visalia around 1 or 2 pm - what would you the rest of that day? If you plan to go up to the park, you'll get two or three hours before dark and then have to make that long trip back down the mountain to Visalia just to sleep.
Kings Canyon has some less expensive accomodations (cabins)- see their park page for details. Any accomodation in the park would be preferable to staying in Visalia, in my view.