We live in St. George, Utah and know that desserted Utah road Twindman mentioned. Gas up in Delta or Ely, depending on which way your are arriving.
Ely, Nevada is about 1 hour from the park. There are a number of RV parks / Campgrounds in or near Ely. Check them out on the web.
If this is a November / December visit to the Park, take along some warm wooleys; you'll need them. Make sure to check the weather forecast.
I don't know when Leman Caves (an attraction inside the park) closes, but check it out on the web site.
Enjoy your trip. You're not going to have to deal with crowds.