There's plenty of hiking trails on the mountain. There's also mini golf, real golf, chair lift tours, and more. In the Village, there's year-round ice skating, shopping, and plenty of restaurants. Check out their website for ideas.
Vail has tons of things to do. You can hike the ski slopes and trails, or take the gondola up to the top and do a ropes course. There's also zip lines, tubing, and a cool roller coaster. Check out the website for prices and things. You can also check out Vail Village, with shops and restaurants.
Restaurant Recommendations in Edwards: Harrison & Hovey - yummy farm to table food. good for breakfast and lunch, open for early dinner Craftsman - great beer and pub food Eat Drink - primarily wine and charcuterie, but with salads and paninis as well Village Bagel - excellent bagel shop for a quick breakfast or lunch.
Restaurant recommendations for Avon: Avon Bakery - great sandwiches Northside Kitchen - excellent breakfast, lunch, or dinner. they also have donuts. Dusty Boot - in Beaver Creek Village, your basic bar food
Thirty minutes west of Eagle is Glenwood Springs. They have a few different hot springs, Iron Mountain Hot Springs being a favorite of mine. There's a bunch of different small pools at varying temperatures, and a separate family pool. There's also Glenwood Caverns Adventures. They have cave tours and a mountain top park with rides - we haven't been, so I can't vouch for it, but it certainly looks cool.