It really depends on what you mean by visiting one of these parks. Do you mean a drive thru, stopping at the scenic pullouts. Or do you mean really exploring the park, hiking trails and so on. If the later pick a couple of them and camp outside (or inside). It takes a week to even get to see some of one of these parks.
I'm always befuddled when I see these people in tour buses. They get driven around the park road, stop at a couple scenic turnouts, visit the park HQ and leave. See three parks in one day. They then cross that park off their list, been there, seen it all.
BK