Two Hands wrote:
Stay in the park! There are about 15 full hookup sites. Just reserve early.
^^^^^ This.
Morefield Campground in the park is highly recommended if you really want to have the full experience of Mesa Verde.
H E R E - Mesa Verde is the link for the camping information, and
H E R E - MV Map is a map for Mesa Verde. You will definitely need reservations for Morefield, so make them early. They use the 180 day window for reservations IIRC.
Stayed there in October 2017, in a FHU site in Morefield. Senior Discount for getting in the park, but no discount at Morefield. $50/night for FHU as I recall. Here are some things I learned.
As previously recommended, stop at the Visitors Center and if you want to go on a tour, that's the place to be. Just make sure you get there before they close, which was around 4:30 when I was there. They can also advise you what specific tours will be available (read as open due to weather or other restrictions). IIRC, you can also get tickets at the Chapin Mesa Museum. The best places to visit require the tour tickets.
Distances in the park are deceiving. It's 4 miles from the Visitors Center to Morefield, and another 11 miles to the Farview Lodge area. Another 5 miles to the major cliff dwelling areas, with 2 loops that are each 6 miles in distance. And that's all just on the Chapin Mesa, the "lower" of the 2 mesas. There's also Wetherill Mesa, the "upper" of the mesas, and it's another 12 miles to the cliff dwellings.
Fuel. There's fuel in the park. It was outrageously expensive when I was there. Depending on the direction you're coming from, fill up in either Cortez or Mancos. The fuel just outside the park is also as ridiculous in price. .50 to $1 more/gallon at these than it was in Cortez.
Time. Give yourself plenty of time. There are plenty of photo ops, and a variety of hikes if that interests you. You can easily spend 3-4 days there and still have things to see and do.
Weather. Late Winter/early Spring this past year saw some record snowfalls in that area, from 800% to 1200% above normal. We had major snows around Memorial Day in northern Colorado, and they had even more down there, so consider your timing and keep an eye on late season storms.