For a long while, I wasn't a skier....then took snowboarding lessons and love it. There are MANY things to do if you don't ski.
Vail offers "foot passes" that allow you to go up the Gondola or the Vista Bahn ski lifts without skis. The gondola is not exposed to the air and there is much to do at the top of the Gondola. Both are beautiful rides up the mountain and both have wonderful restaurants and beverages. I used to bring my book and enjoy the sunshine and atmosphere. My hubby would meet for lunch. There are photographers at the top of the lifts that will also take your picture. The picture taking is free.....and if you like the photo, you may purchase it for a $$$ fee.
There is a really cool library in Vail. It is across the street from the skating rink. They have a few PCs with free internet...but those were usually hard to get. The skating rink sometimes has exhibitions, but mostly it is hockey teams practicing (and those are not usually open to the public).
Many of the spas offer a day pass for their exercise equipment. I don't know if that is of interest...but I used to enjoy a good work out, then sitting in the steam room.
The hotels (in particular the Sonnen Alp) have wonderful lobbies. Some serve afternoon tea. Again, I used to bring a book and hang out....talking to strangers or ordering tea.
The Sonnen Alp also has a terrific spa (with outdoor heated pool) and full spa services. I enjoyed that experience.
There is a movie theater (with four screens, I recall) that SOMETIMES offers matinees. There is also one out at the hotel (can't remember the name of it)....which is a short shuttle ride away.
Lastly, Vail has a TON of little shops to poke into. The people are friendly and laid back.
Enjoy!