1) Get ready for the elevation.
Plan your trip smart! Be well rested before your arrival in the mountains. Remember you're going to need to acclimate to the elevation to reduce strain on your body. Experts suggest even just one night at a "mid level" elevation such as Denver can be very beneficial for your body to adjust to the high country. Ever notice when you breathe into a the nylon collar on your vest or jacket, a little moisture accumulates? That moisture has just left your body. So keep in mind that with every breath you take, you're losing just a little bit of moisture. Dehydration caused by the lack of moisture in the higher elevation is one of the main culprits causing altitude sickness. Start drinking more water the day before your trip - 2 to 3 liters per day is the recommended amount. And don't over do it on your first day, take it easy and avoid that gondola ride up to 11,000 feet, if possible.
2) Consider this: You might not need a car.
Free public buses in Vail couple with complimentary hotel shuttles and heated streets to create a pedestrian-friendly paradise. Buses run all day and can get you anywhere you need to go (including Beaver Creek!) Check in at the Vail Welcome Center, located above the Colorado Ski Museum, upon arriving to town to get all the latest info on shuttle schedules and pedestrian options. If you're arriving directly in Lionshead, you can find another welcome center there at the bottom level of the parking structure. The friendly attendants there can help you plan every aspect of your trip; and if you do need to book a cab for any extraneous travel they'll be happy to do it for you.
3) Remember you're a lot closer to the sun.
Plan on taking your sunglasses with you and don't forget to reapply sunscreen throughout the day no matter of the season. At Beaver Creek, you'll find an unlimited supply of sunscreen right at the base of the main Centennial lift which is free to use. In Vail, you may have to venture all the way to one of the more luxurious lodges on the mountain, such as the Two Elk lodge, but if you let them know you're a paying customer they'll find the free sunscreen for you.