Two weeks RV road trip

You're going to need to run the air conditioner at night and that means full hook up sites. You won't make any friends boondocking and running a genny all night. You're going to need to make reservations, and it may already be too late for July 4th.

This is extremely important--good advice. We were in Italy in June of 2009 and we found nothing to compare with the heat in the American South and Southwest. You will need electricity to run the air conditioner.

Taking Los Angeles as a given, I would suggest heading straight up to Sequoia/Kings Canyon--about 200 miles and four hours. That makes 2 nights in Los Angeles and a minimum of 2 nights in Sequoyah.

If I were that close I'd add in Yosemite. You will probably have to find a campground outside the National Park, but Yosemite is one of the outstanding parks in the United States. Add minimum 2 nights

Again, taking Bryce Canyon as a given you've got a two day trip across Nevada (I'm bypassing Las Vegas for the moment to go straight to Bryce.) There is a northern route along US 50 which is known as "the loneliest road in America," or a southern route that dips down via Hawthorne, NV. Add 2 nights for overnight for two long days (about 650 miles total).

At Bryce for 2 nights. The drive down to the North Rim is just over 100 miles so you can get a good view on the afternoon of arrival. We stayed out at Jacobs Lake, but that is a good 45 (slow) miles into the rim. Still we had a long afternoon to get view all along the rim and wound up at sundown at the lodge, before returning to our trailer waiting out at Jacobs Lake. So you can add 1 day here.

Around to the South Rim is less than 200 miles, so a relatively easy drive. May as well see both "rims" so add 2 days here.

We are already up to 13 days and that's by moving on more than many would advise, but it's entirely possible. That brings us to Las Vegas and July 3. This may be a critical decision of your trip: where will you be on July 3 and July 4? I'd bypass Las Vegas and
scoot across to Antelope Valley (or a non-urban campground nearby) and spend the night.

Now, unless I've messed up the arithmetic you would have only one day to get your RV back to Los Angeles. (I'm not good at math!)

If I can help with any more specific questions about this route, you can send me a PM (private message) through this forum.

That seems to me about the most you could include in a trip of 15 days in this part of our country. You may have very good reason to want to include Los Angeles, Las Vegas, and the Southwest National Parks, but someday I hope you'll consider a visit with Denver as your starting point (in the Summer, of course) and enjoy the cool, colorful mountains of Colorado instead of the hot Southwest.