How to visit the Parks
Decide on the must-dos and how long you want to stay. Don't dismiss the smaller parks with shorter visits. Take the time to understand what they're offering. Some parks do have smaller offerings (Sand Dunes or Black Canyon Of The Gunnison) that you could theoretically do in one day, although even for Black Canyon, I would have wanted a second day to be able to get down to (or onto) the river in the canyon.
Hit the web site. Download the park maps. Go buy topo maps from REI or online. Read the library travel books on the area. Decide on the must-dos. Develop a visit plan, but don't be limited by it. Some things show up when you arrive that you'd never know from the guidebooks or the web sites. Sometimes you're in the place and you realize that that one big thing you thought was the jewel of the park is like the Trevi Fountain - nice to see, but not the glittering gem you imagined it to be. Instead, you'll find surprise and excitement in unexpected places. Perhaps you'll drive through a State Park that sparks your interest and you'll prefer to explore that park in more detail.
When arriving, get a good photo of yourselves standing at the park entrance by the sign. Don't get run over! This is more fun than it sounds because you're usually balancing cameras on rocks, cars (not always your own car), fence posts, hiking sticks or fellow park visitors. In many ways, getting the entrance picture sets you up for your experience. You often meet people who are as excited as you are to visit these special places, all as keen to get a picture of themselves at the park entrance as you are. This is a prime opportunity to grab someone's camera and make off with it!
After getting your park entrance picture, hit the visitor center (if there is one, lol Alaska lol). Engage the rangers and look at the hikes, lectures and events being offered. Each park is different. At Great Basin, there were many evening events focused on Dark Skies where people brought their own telescopes. GB actually has astronomer park rangers specifically to enhance and enrich the Dark Skies experience that many visitors go there for.
Then, develop a walking plan. This is perhaps the best part -- you're going to be amidst the forests, on the dunes, inside the canyons and amongst the glades. Great Basin's Johnson Lake Trail on the Snake Creek Road is an example. You quickly ascend into groves of the biggest Aspens you've ever seen. You need to get onto the land to see these things. The walking is the biggest part. Do it justice by planning your walks with care. Ask the rangers, but be adventurous.
Include any side attractions. GB, again, has the Lehman Caves, which themselves are interesting, but perhaps a side attraction. I'm glad we did the Caves because they're a fairly significant attraction in their own right, but I would have said that GB's best side is the land and the scenery.