Tennessee to Colorado

That's a long drive for one day (10 hours). We usually drive 5 hours and stop. In Kansas City there's Worlds of Fun that has RV sites. I would call and make a reservation as soon as you know when you're leaving. Weekends (Fri & Sat nights) might be a problem as well as holidays. Also high tourist areas like Estes Park will fill up during the summer. There is a KOA in Salina KS that would work for an overnight stay. I would not arrive after dark. For Estes Park, you could stay in Loveland and drive over. That's what we do if the high tourist area is booked.

We often stay at KOAs, but they are just one of many options. I check rvparkreviews.com for the area we will stop, find an RV park with good reviews, and call ahead to see if they have a site available.
Unless you will be in a really touristy area you will probably not have a problem finding a site, especially if you call before too late in the day.
Keep in mind that June in Colorado can still be quite cold, and often windy. We have been to south central Colorado the last 2 weeks of June the last 10 yrs. morning temps have generally ranged mid 30's to low 40's, daytime highs 60 to mid 70's.

You can also log onto Good Sam web site and use the Trip Routing option that they offer. When in the program you can select the option to show campgrounds. Then you can specify GS parks, Private campgrounds, Public campgrounds or all of them. Then just click on one shown and see its amenities. Tim

The KOA in Estes Park is nice and was completely unaffected by the flooding in Estes. June is prime season for them on weekends, so reservations can be tight. If you're planning on staying there upon arrival, try to get your reservations in as soon as you can. If you're open to other places in Estes, again you'll likely need to make advance reservations. You might want to consider Mary's Lake CG, it's a county-owned facility with diverse spots from dry to full hookups. BUT it can be very VERY windy there. In spite of that, we stay there frequently throughout the season. The rates are very reasonable compared to other Estes Park locales.

There is a park on the east side of KC next to an RV dealer right off of I-70. The park at Worlds of Fun as mentioned before. There is a simple park near the Kansas Speedway on the west side of KC. Lawrence has a RV park plus a nice lake. There is a casino RV spot near Topeka. Salina has a KOA. I'm guessing KC is about as far as you might make it from Tenn.