For a first time visit I'd suggest the South Rim of Grand Canyon. We enjoy the North Rim for the quietness but we've been to the South Rim often. There's lots to do there. Try for a site in Trailer Village near the rim. The free shuttle stops just outside the campground. If you don't need hookups your 28' would fit in Mather, a very nice shaded campground near Trailer Village. There are showers available.
I certainly would not try to do day trips from one park. It's a lot of wasted time and miles and how many trips would you really make? These parks deserve more than a few hours. It's not difficult to move from one area to the next.
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