So many choices.
Some rag on Tahoe, but I love the place. If you do Heavenly, you'll have South Lake Tahoe at your disposal. That is a full-on resort town with tons to do during your stay. If you're staying for 10-14 days, I assume you're going to want tons to do. When Staying in South Lake Tahoe, Heavenly is right there. The snow is just so-so, but those on the lower end of your group will enjoy it. You can also catch a shuttle bus every morning to Kirkwood or Sierra At Tahoe. Both are killer spots, with Kirkwood being more of a Snowbird-esque (Double-Black) mountain. Easter is April 8th, so if you're going the weeks leading-up to Easter, you should be golden. Later in April is more of a crap-shoot. (Airports From Reno-60 min Drive, From Sacramento-90 min Drive)
Summit County, CO would be good if you stayed in Breckenridge or Vail. Neither town is as big as South Lake Tahoe, but there is plenty of fun to be had at both. I would assume it would be a bummer to vacation in Dillon or Frisco without a car, especially for 2 weeks. The Public shuttle system is good in Summit Co, though. As others have said, Def Check out the Epic Pass. It'll get you access to Vail, Breck, and Beaver Creek, and I think A-Basin. That'll keep you very happy for 2 weeks. I've had hit-or-miss snow experiences in Colorado. Don't use this year's snowfall as a basis because it was surely an anomoly. Getting to Summit Co from the airport will cost you about 60 bucks each r/t via a service like Rocky Mountain Express. (Summit is 1.5-2hours from Denver International)
SLC: It is difficult to go wrong with SLC, though it could be pricey. There are premier resorts, the snow may very-well be the best snow on earth, thought the towns are eh. Again, for 2 weeks, you're not going to want to stay at Snowbird. It is surely nestled-away from the rest of the hub-bub. I hate to suggest staying in Park City, but the town is a good time. The Canyons Resort and PC Resorts are good, but definitely not the Caliber of Snowbird or Jackson Hole. If you don't stay in Park City, check-out staying somewhere in Salt Lake City. I know the bus system is decent, but I don't know it that well. (Can get from the Bird to the Airport in 40 mins)
Jackson Hole. Premier Destination that is difficult to get to and is known to have some of the gnarliest terrain in the States. But....once you're at JH, you probably aren't going to too many other resorts. JH is pretty much it.
Good Luck, Have Fun, and Suck it up and rent a car or two!
Traveling the States and Taking Pictures