While not as convenient, it is possible to fly into Denver International Airport (DIA) and get around using only public transportation. The Colorado Mountain Express shuttle (ridecme.com - 800-525-6363) goes from the airport to Dillon and other towns in the area. It costs close to $100 per person so if there are two or more going it would probably be cheaper to rent a car.
Once you get to my condo there is a free shuttle you can use (summitstage.com).
It goes all over Summit County - Dillon, Silverthorne, Keystone, Breckenridge, Frisco and the ski resorts.
There is a bus stop right next to the Arapahoe Cafe which is at the northeast corner of the Lake Cliffe condo complex.
There is only one taxi service in the Dillon area and they charge about $20 just for the pickup and then extra to get you to where you are going (453taxi.com).
Following are some distances from the Lake Cliffe condos.
Grocery Store (City Market): 6 blocks, about 1/2 mile
Lake Dillon Liquors (970-468-8006): 6 blocks
Ski rentals can be done at each ski resort - probably the easiest without a car. However, renting your skis from a single rental place for the duration of your stay is probably cheaper and you'd have the same equipment for each day.