camping

Is May a little early to go?

No reservations here. Not even for Grand Teton National Park over the July 4th holiday last month.

The trick is to get where you are going by mid afternoon. Get someplace for the weekend on Friday & sit tight till Sunday. Oh yeah, be flexible. If plan A falls through, have a plan B. If that fails too there is always something, even if it is Walmart.

We have rolled into the Grand Canyon south rim with no reservations too. Also Yellowstone Bridge Bay CG, no reservation.

The FHU & pull through sites go first, then the W/E. If you can survive a few days dry camping & know how to reverse, getting a no reservation site becomes much easier.

As mentioned, make the reservations for the NPs, but give yourself a few extra days in between,so you don't feel like you are rushed.
Getting to a CG within a half-day of Yellowstone, will allow you to be relaxed and not worry for that last days drive.
Plan for the unexpected! Better to be there a day early, and spend the night at a Walmart, than to be rushing all day because you had a blown tire.

Sometimes, it's nice to set up your trip to camp about a half-hour from the sights. Most folks will want to be as close as possible, and those places will be packed. Get a bit outside the loop, and you may have more success.....and you can camp the night before, then get an early rise to view the sights...then head back to the CG to relax for that night.

I make reservations at our destination. While enroute we just wing it. I'll use Free Campgrounds and Free Campsites or another free/low cost overnight stop. There are several web sites available, just do a little research.
I would definitely make reservations at the National Parks.
Enjoy your trip.

For any of the major attractions: Yellowstone, Mr. Rushmore, etc. you will need to make reservations because they fill up very quickly. I made reservation for the south rim of the Grand Canyon 8 months in advance. I planned around that and in 34 days on our trip I only made reservation for 10 total days.

Hard call...but summer and popular national park destinations - it may be wise to make at least some reservations.