I see you live in Canterbury, Baldrick. Where do you ski locally? What are your favourite runs? Least favourite?
Also Cantabrians, we've skied a bit in Utah (plus a side trip to Jackson Hole) over the last few years. We haven't been to Colorado yet, or Tahoe, so I'm not going to be any help there, but it looks like there's plenty of good advice on that above.
Each of our trips annoyingly coincided with low snow cover (for Utah) and dry spells, so we're quite familiar with the worst-case scenario. However, low snow cover in Utah is not like low snow cover here. You'll still be able to ski, almost certainly without risk to your health or your skis. There may however, be hardpack, verging on ice, and certainly bumps, and some runs might be closed. But because of the altitude, there will still be snow on the ground, and even off-piste won't be completely off-limits.
Salt Lake City is a good hub to fly into, and drive from. Almost all ski areas in Utah are within an hour and a half's drive from the airport. Jackson Hole took around 5 hours to drive to (it was a while ago, so that's a bit of a guess, though we weren't in a hurry).
Assessing mountains on their scenic potential is fairly subjective. In NZ, we're used to seeing rugged mountains rising quite dramatically, almost from sea level. But they're lower in altitude, and the snow line looks quite a lot higher. Some of the inland ranges in the US appear less dramatic maybe because their bases are already at a high altitude. But that aside, there is some impressive alpine scenery in Utah (less so on the Park City/Deer Valley side of the Wasatch). For spectacular scenery, the Sundance resort (Mt Timpanogos is a beauty) further south is pretty cool, but Alta, Snowbird, Solitude and Brighton all have great views of rugged peaks too. Snowbasin also has excellent views -- the fog hanging over the Great Salt Lake from the top of the little tram is certainly a sight. Mostly it helps to be experiencing the views from up high, as opposed to looking up from below. Although Jackson Hole is rather scenic to look at.
All of them have tree-lined runs, though some (e.g. JH, Snowbird) have sparse to no tree cover at the tops, where the wind can be "bracing" at times. But there are alternative lifts to take when the weather is challenging.
I've only spent two days at Snowbird (where we were taking part in an off-piste clinic) and I didn't see that much in the way of cruisy groomer runs there. But then Alta, next door, has some easier skiing, and you can ski between the two resorts if you have the right pass. Often conditions can vary quite dramatically between the two, so it's nice to have that option. Off-piste skiing at both areas is fantastic and as gnarly or mellow as you want it to be. Big Cottonwood Canyon (Solitude and Brighton) is smaller, quieter, more low-key, but the terrain and snow conditions aren't that dissimilar. Maybe not as rugged and exposed up high.
Snowbasin is a bit of a gem. It's further from SLC, so it can be very quiet, and it has fun and easily accessed off-piste, which can take much longer to get tracked out than resorts closer to the city, plus some fantastic wide, long groomers. It hosted the 2002 Olympic downhill, so there's a decent vertical. The lodges are quite OTT luxurious. Snowbasin has decent snowmaking, which came in handy the first time we visited. Snow conditions can perhaps be a bit more variable than the others, but when its good, it's very good.
The Mountain Collective pass covers Alta, Snowbird, Snowbasin and Jackson Hole, plus a variety of other locations. If you have the 3-peak nzski.com pass, you already qualify for half-price skiing at those places. If not, Liftopia etc can be useful.
Park City is on Vail's Epic season pass which is probably more useful for a Colorado trip. I'm not sure I'd necessarily detour to Utah just to ski at PC. It's not that there's anything really wrong with it and it makes a good longer-term base (I spent a month there a couple of years ago) but there are definitely better nearby ski fields if you're planning to sample a few.
Deer Valley owns Solitude. There may be some pass benefits with that -- I haven't looked into it.
Skiutah.com can be a useful, centralised source of info.