Hello and welcome to the RTA forums !

You have a nice amount of time for a great trip and what you have mentioned is doable as long as you are happy with the pace. The first thing I would consider is to make it a loop trip and start and finish in the same city. Not only will it save you the rather large one way drop off fee, it will also give you more options to find the best flight and RV costs to any one of the City's you are visiting. For example if you started in SF and headed down the coast you could head to GC > towards Denver and RMNP with places like Monument valley, Arches and Canyonlands NP to consider. From Denver [Rocky mountain NP] you could then head to Badlands, Rushmore etc and to Yellowstone NP. From Yellowstone through the Grand Tetons to SLC and Bryce and Zion NP's. Then you would head towards Yosemite NP to include Vegas, or not. I doubt you will be allowed across Death valley in the summer in a rental so you could cut across from Zion towards Tonopah and Lee vining and enter Yosemite over the Tioga Pass. Then Sequoia NP back to SF. Of course there are many ways to work this and it's just set as an example of doing a loop without back tracking.

Some parks can be seen quicker than others and a couple of nights in each of Yosemite, Zion, Grand canyon is really the minimum needed to appreciate them. I haven't been, but Rushmore could probably be an afternoon visit and Yellowstone would be at the other end of the scale where you really need 3 or 4 nights to get around this huge place. Bryce can be appreciated in a full day which would mean either 2 nights or just the one night and an afternoon and following morning. This is a 'minimum' really and you could easily spend a week in Yosemite [for example] and see new things each day.

When renting an RV you need to make sure you get the bottom line figures and know what is included and what isn't. Mileage charges, Insurance fee's, bedding and kitchen kits, preparation fees etc and if it were the case, the one way drop fee. Cruise America often have specials for longer and local rentals [same drop off location] and you can find them by clicking in their 'Hot deals' link on their own website. They often include insurance cover in their fee's as well. It's not to say you can't find bteer deals, but they are usually are competitive when you get down to the fine print.

The one thing you need to know is that RV sites in National parks are limited in number and extremely popular. High demand means a lack of available sites and booking is highly recommended at the earliest possible time, when that booking window opens !