If I was you and this was my first road trip in the US I would do a little trip south of San Francisco to take in Carmel, Big Sur and Hearst Castle and then a route which takes in Yosemite, Vegas, Bryce Canyon, Monument Valley, Grand Canyon.
We’ve done a few road trips like this. My favourite memories are always those from the National Parks and coastline south of San Francisco, Arizona and Utah. It’s all spectacular!
You’ll have to decide if you want to see San Francisco. I haven’t been to LA but I’m not sure if I would go back to San Francisco again. It is not the city it was on our first visit 30 years ago and it is really expensive. Of course if you are flying all that way it is a shame not to see such an iconic place though. Two nights felt plenty last time we were there.
For our most recent road trip in 2016 we flew to San Francisco. We stayed 2 nights in a corporate style hotel on Union Square. Lots of people prefer to stay down at Pier 39. We went to Alcatraz and hired bikes and cycled over the Golden Gate Bridge. We then flew to Vegas and stayed in a casino for a night - the casinos are good value to stay in because they want the punters but I seem to recall the nicer restaurants were still quite pricey. Our youngest child was only 7 at the time so we saw a Cirque de Soliel show and spent the afternoon by the pool.
We have generally used Vegas as a leaping off point for a few different road trips staying in a mix of motels, hotels and national park campsites - on our last visit we packed two 2 man tents (we have 2 children) and bought camping supplies in an REI camping store in Vegas. We have also driven from San Francisco to Yosemite on previous trips and taken routes on from there.
Would you consider camping as part of your trip? Staying in the National park campsites is cheap and it’s amazing to be sleeping right under the stars in Bryce Canyon, The Grand Canyon, Yosemite, Sequoia, Arches, Zion etc when the other day trippers have left. The parks have twilight Ranger talks and walks and the bigger parks even have supermarkets. There are grills / BBQs at each camp site for each tent pitch. Our experience is that showers and toilet blocks are well maintained.
We usually buy fairly cheap camping supplies like the stove and give them away to other campers on our last day. We pack sleeping bags but they squash down small and are light enough. It’s easy to buy ice for cool bags too.
Monument Valley is incredible but the campsite is really terrible - if you can stretch to staying in The View hotel you won’t regret it. We have always arrived in Monument Valley via the Mokee Dugway but this is absolutely not for the faint hearted as it is a sheer downhill hairpin bend track down a massive cliff - there are other much more driver friendly routes to get you to Monument Valley but they are not as spectacular.
The most recent roadtrip was in 2016 and we spent £12k over nearly three weeks including flights and car hire. We got a travel agent to book the flights, car and our hotels and we sorted the camping in the National Parks ourselves. We did have family rooms in some motels but we also splashed out on 2 rooms in hotels in Phoenix and Tuscon.
Last summer we went to San Diego for 2 weeks and did not hire a car. We stayed in an apartment hotel quite near the zoo and used public transport to get everywhere. It was really noticeable how much the prices had gone up - that trip also cost us £12k in total including about $220 average per day spending money for just three of us, as our oldest child didn’t come this time. I don’t think we would have felt like we were really on holiday if we had budgeted for less spending money, so do look at cost of entry fees, eating out (even at budget places), fuel / public transport etc. Cities are expensive but the beach days in San Diego were less expensive than the sight-seeing days. The ability to sort our own breakfasts in the apartment and the occasional packed lunch or lunch in the apartment helped a bit with costs.