I haven't made it to Yellowstone, but have gone to Seqouia NP (snow + massive trees) Zion NP (well worth a look, impressive rock formations), Death Valley NP (it rained and snowed
! found it dull, but a tick in the box) and Grand Canyon NP (-7, snowed, photos do it no justice at all).
We were on a budget, so they were mostly day trips out of Vegas, except for the Grand Canyon where we walked 1/3rd of the way down to the river and back again, stayed over night and got up really early to see the sun rise.
Organized tours certainly have their good points, in that they take you to the popular spots, but you are also trapped with the tour group, so you stay longer at a spot that you may think is necessary, or have to hurry off because the group is leaving. You generally get corralled into areas that have easy access too, which is good if you have a dodgy hip, not so good if you are active and want to explore.
If you haven't been to a US National Park yet, you will be astounded at how geared they are to tourists, unlike ours that see tourists as an inconvenience. There will almost certainly be an information center, apart from the gift shop, so stop in there, talk to the Rangers. There will be maps available to direct you to the good spots and the rangers will direct you to spots that you can't get a tourist bus into that might also be worth a look.
If you are there in warm weather that coincides with a holiday, prepare for massive crowds. Some mates went to Yosemite and were stuck in a traffic jam that crawled along at less than a walking pace, water bottles in the boot are a good idea. In that situation a tour would be an advantage as they get priority parking to get you in and out.
