Some years ago we passed through in early June. We came from the south (Nakusp hot springs), spent a night at a prov. park south of town (Rabbit Blanket?). Then drove into town and bought a park pass, and did some grocery shopping. Then drove up the mountain as far as snow would allow. (this was in an suv so the mountain road was not problem).
Then back to town, and north to another Prov. park on a Columbia River reservoir. I don't think there was any car camping in Revelstoke NP itself. There's a private campground off of Hwy1 with a hot springs, but I was told is was pricey for what it offered.
The next day we had breakfast in town, and headed east on Hwy 1, stopping at all the day hikes along the way to Rogers Pass. We got to the pass in time to share our lunch (not) with the ground squirrels.
Then nonstop to Yoho NP. Kickinghorse campground was full (except for the overflow), so we drove on to Lake Louise and got a spot in in the fenced in car camping area.
On a later trip we visited Yoho from the Banff side, and stayed in the Kickinghorse overflow, and were happy with the time. There's a enough hiking there. And if your RV or tow/toad is small enough the drive to Takakkaw Falls is well worth the time. This has the only true switch backs on a paved road that I've seen (vehicles longer than 7m have to back up the middle leg).