My advice (the second post from the top) to wait for snow was based upon having a romantic and visually stunning trip, not just skiing. The beginner slopes should be covered OK with snow making if Mother Nature is tardy with the real stuff, and you can get great "Never-ever" or beginner lessons anywhere. But when on vacation an area covered in snow puts a bigger smile on my face than one that isn't covered in snow.
All things being equal, Vail village is perhaps more romantic and easier to walk around (no alleys for one thing) because it is a village . And yes, you can get a bus back to Beaver Creek at night. Both Hyatts are beautiful, although I kinda love the chandelier in the Beaver Creek lobby. Walk out the door and you are skiing Beaver Creek. The Rockies covered with snow against a blue sky is always a "KODAK Moment." As Cirquerider pointed out, there are a zillion places to ski around the Lake Tahoe, and most have visually stunning views of the lake. UGASkiDawg assumes Vail will have a better quality of snow in December. He is likely right, since Vail does seed clouds. Regardless, as beginners you aren't going to ski knee-deep powder.
It will likely be less expensive to ski around Lake Tahoe providing you get a rental car or can put up with a bus. You can likely ski three days at a smaller resort like Homewood with killer views of the lake for the price of a Vail/Beaver Creek lift ticket (I don't know what kind of deals there are for beginners in the Vail area). SHREADHEAD thinks you should wait until Thanksgiving until booking your flights. It may not be a bad idea.
Regarding a six-hour private lesson? It can't hurt. Assuming you are a brand new skier, check and see if there are any ski schools offering a "Never-ever" type of lesson package. You can get a pass, rental equipment and a group lesson heavily discounted with these types of lessons. It may be worthwhile on your first day to do a never-ever while you are still getting acclimated to the altitude.
Either location is the foundation of a world class vacation. I am envious of your free rooms!