Almost every races to Blue Sky Basin as soon as the mountain opens. You want to get there early and get out early as well. Lover's Leap is the favorite run of many at Vail so make sure to ski it at least once. After that, I normally go ski around China Bowl for awhile. The trees under the Orient Express are a lot of fun.
In the afternoon, I usually lap the Golden Peak Terrain Park. Compared to the other Colorado mountains, it's not a very high quality park. However, it's almost always empty, and the chairlift rarely has a line. If you're trying to get to the park from the top of the mountain, make sure to go to the top of the Riva Bahn lift and download to the halfway point. If you don't do this, you'll have to take another chair up before you get to the top of the park.
I don't know how much money you have for food, but if you can afford a $20-$40 dinner, go to Alpenrose restaurant in Vail Village. They serve Americanized German food, and it's absolutely delicious. If you're thinking about going to any of the pizza places in Vail, don't. They're all mediocre and overpriced.