Since the MCP is a dual mountain pass already, talk to some locals, or patrol people when you get there. One thing that is worth a quick run or two is dropping into mineral basin if the snow is good. Very little traversing to get in and out and it's not much time spent getting back and forth.
Also MCP does include hopping on a local MTA bus so if you do get stuck on one side you can still get back to your vehicle without too much trouble.
That being said, unless I'm meeting someone over at Snowbird, my choice is Alta every time. I love the small mountain feel. It's just a little higher overall in elevation so the snow tends to be a little lighter many times.
There's just so much charm there.
One thing that's a must do at Alta especially if you are starting to get up in age (I think the OP said 61) is to go meet the "Old Wild Bunch" they are a great group of Sr's that meet almost every day late morning for lunch at Alf's Just go say hi and be inspired!
The Old Wild Bunch are easy to spot at Alf's. Start by looking for someone with a badge that is for "70+", then look around for those with the "80+" badges. Great fun to hear the discussion outside from a Wild Bunch group trying to decide which trees to hit based on where they skied before taking a break. Or a few fussing in the spring because things hadn't softened up yet off the groomers.
If the OP does decide to start at Snowbird on the first day and visibility is good, could head over to the Alta side from Mineral Basin for a quick preview by taking a ride up Sugarloaf. Can see more than enough of Supreme trees in the distance, Devil's Castle, and the Backside to have some impression of how much fun there can be. Especially if can spot a few folks heading down to sense how far away they are.