Hi Gina - we'll probably talk about this a lot before you leave Q, but a couple of things come to mind. We love The Valley of Fire campgrounds within the Lake Mead Nat'l Monument area ... the geezer/ADA pass works and they have flushers and showers. It is just north of LV, east of I-15. The closest burg is Overton (good ice cream!) and there is an interesting museum showcasing the "Lost Cities" covered up when they built the da** dam- oops, sorry
And between The VofF and Overton there is a bluff the locals call Poor Mans Bluff - lots of dry-camping with awesome views. You'll know it when you see all the RV's scattered around.
We've heard St. George, UT has some nice camping country but haven't visited yet. Lots of history here.
Cedar City is a nice little town - lots of history here too. Too bad you will travel early in the Spring - they have a terrific Shakespeare Festival all summer.
I don't remember any bad grades, but I've slept since then, so ... the hills I remember were doable, and that was with the Mazda before we got "Ovrkyll"
North of Salt Lake City, if you leave the interstate & go a ways West, you can visit the site of the "Golden Spike" that completed the nationwide rail system ... I think you can camp there too.
As you pass thru some of the small towns on the 15, you might check about parking at the curb in a city park. We had good luck in Delta, but that's not on the highway.
If you're not averse to 'pavement camping' there are some decent truck stops along the way as well.
More later, as my remember-er gets workin'. LdB