Since you have a week, you can try several locations. I think one of the best lesson and learn to ski plans is at Sierra at Tahoe and you can also ski Sugar and Spice. This is a 2.5 mile beginner trail that has nice side trails off of it that can up the challenge a little at a time. Sierra also has a good ski school, and a great 3-day learn to ski guarentee
3-pack beginner package that includes lessons, rentals and lifts at $43/day. That is cheaper than just a lift ticket. If you can do this on 3 weekdays, you should end up with a nearly semi-private series of lessons and skiing.
For a change of scenery, the new TimberCreek beginner area at Kirkwood is very nice. Its served by its own high-speed quad and another slower chair. Its a large dedicated beginner and intermediate area, and you should have the place almost entirely to yourself. This is farther from SLT, but I think is the best beginner area around. Kind of surprising considering Kirkwood is known for expert+ terrain.
Heavenly has beginner areas at the California base, in the Powderhorn / top of the Tram area, at the top of Gondola, and in Nevada at Boulder. These areas are separated by intermediate and advanced terrain. So while it sounds like a lot of begginer terrain, you can only access it one area at a time. The advantage is that each of these areas has lodge, dining and bar services. Personally, I like the others better as a ski experience. Timing...Avoid Sierra on the weekends, Heavenly is better than Sierra on Saturday and Sunday, and best on weekdays. Kirkwood will have the fewest people on any day.