Sorry I couldn't reply earlier, I was on vacation for the past four days. (We have toddlers; it's a good time to go after Memorial Day but before school is out.)
I love geysers, so I would try to see a few. If you can't see Grand, Great Fountain is a reasonable substitute, but it depends on the timing of the eruptions (i.e. night vs. day). In the Upper Geyser Basin, Beehive is very regular and predictable; I never saw it up close but I saw it three times from a distance. Castle Geyser is usually active to some extent; the steam phase is cool. Daisy is a good solid performer with several eruptions a day. Riverside is somewhat predictable and a bit of a hike to get to. If it fits the schedule, see it; it's sublime.
In Norris, Echinus is the most regular geyser, and it has a unique seating "ampitheater" that allows you to look practically down into the geyser while it erupts.
Your itinerary partly depends on where you want to stay. One way to do it would be to go up to Mammoth on day one (you might have to see Mammoth on the morning of day two); then loop back down on the Tower Falls side down to the lake, and see what you have time for at that point. You might want to book a day in a hotel outside the gate at Mammoth to make things easier. Personally, I wouldn't want to drive up to Yellowstone twice from Jackson; it'd be tiring.
Thanks for all the info. You've been a tremendous help. We are really looking forward to it - I feel like a kid on Christmas Eve. This will be our first real vacation since our honeymoon five years ago. What better way for us to spend our second honeymoon than by seeing the splendor that makes America what it is.