I would definitely recommend Arches and Canyonlands NP. Canyonlands is actually 3 segments (Island in the Sky, Needles & The Maze) with independent entrances (you cannot drive across Canyonlands). Arches is at least a day minimum by itself since some of the Arches you have to walk to (a lot of short 15 minute hikes on good ground).
Spend time if you can taking some of the shorter easy walks in both parks, you'll be surprised what you find in both parks for views and history.
We just had time for Canyonlands - Island in the Sky, but did take the Mesa Arch walk - spectacular views. Spend some time on the drive at a lot of the vista points, some very interesting history and ranger talks. You can see a lot of Canyonlands on the paved roads, unless you like long 4x4 trips (some of the 4x4 roads are one-way for safety).
Just find a place in Moab as a home base to visit Arches and Canyonlands. The town of Moab is interesting, but we just used it for home base to go to the parks. Good town services.
Also, go to NPS.gov for information on all the national parks in Utah. There's a lot more parks, etc in Utah that are also very interesting.
Watch Yellowstone NP website, currently the road won't be open through to the Tetons till around May 12th (west side of the loop past Old Faithful). You may want to consider reversing your route - go directly south, THEN back through the Tetons & YNP. Then all the roads in YNP will most likely all be open later in May, especially if they find avalanche damage after they remove the snow.
