Hi Gregg. Welcome to the forum, as you've learned there are a lot great fisherman to gleen advice from here.
I'm in Missoula and will stay clear of the Bozeman/Yellowstone area since there are quite a few people here from that area that know a lot more than I do.
There are many places to camp along the 40+ miles of public access along the Creek, but you will be limited to the campgrounds, and possilby to the distance you can go by the size of your motorhome. The Rock Creek Road is paved for the first 10 miles (beginning at I90), but even in that stretch there are some narrow parts and tight turns. The closest campgound, or first one you reach is Norton
, I think it might still be on paved portion of the road (or very near). As you can see in the FS link, they do not reccommend any sort of large vehicle on the road. That doesn't mean that people do not do it, of course. Depending on the scale of your rig you could make it to Norton. The big RV type coaches really have no business on that road anywhere, though, for the the safety of everyone involved. You have to understand that it is a really busy place in the summer, quite a few stretches of single lane road with turns. I've had more than one sketchy encounter on that road - creeping around a high hair-pin turn to meet another rig head on - then having to back down a very steep grade to get to a pull out...ugh...And the road itself becomes a brutal washboard.
I'm not trying to discourage you, but you have to know. And like I said, it all depends on the size of you motorhome. If you can get into the first campground at Norton, the number of miles of river to fish is only limited by how far you care to walk. It is such a beautiful place that any spouse would be content just sitting and reading or walking up the road.
Final thought: mid-June will be hella-crazy-busy with peak Salmonfly hatch - fishermen come from everywhere. Plus it is the only time of the year that people can float fish the Creek. And depending on our spring weather but odds are very good that the creek will still be very high mid-June which makes very difficult/dangerous wading. I would reccommend waiting till the first of July for a safe bet. When Rock Creek is running high, you won't be doing much wading.
Gallatin offer tons of wading, good access and easy camping. Big Hole is a great wading river.
You are sure to find plenty of places that offer ease of access (for motorhome camping, to rivers, to fishing), garaunteed. Don't limit yourself you a strict itinerary and you will have a blast.
Good luck and keep in touch. Feel free to use the PM function if you have more questions specific to Rock Creek or the Missoula area.