That time of year you could probably walk into some hotels and book a room, and in others it would have been better to have a reservation. A few weeks later and you could have your pick of places, as many of the tourists gone. While online reservations can be convenient, sometimes it seems the least expensive option is to show up unannounced.
Of the places you mentioned, I'd recommend something centrally located to them all. Two places come to mind, both in Frisco, CO.
The Ramada Limited
Ramada Limited Frisco
is on the edge of town, next to I-70. Very easy access, and if a room on the sunny southern side you probably will not hear the interstate. Lovely views as well. Moderate prices, at least for that area. Modern, nice rooms, if small. There is a Safeway grocery and some restaurants within an easy walk; a bit more of a walk on a lovely town trail can take you into the center of town.
The Snowshoe Motel
Snowshoe Motel, Frisco, Summit County, Dillon, Breckenridge, Keystone, Colorado
is located in downtown Frisco, on the main street. More of a traditional two-story motel, but nice enough. Comfortable rooms, larger than at the Ramada Limited. Price is moderate, roughly equivalent to the Ramada Limited. The location may decide you, as it is a pleasant and easy walk to anywhere within downtown Frisco. They have a lovely main street, with many beautiful shops and restaurant options. These, on the pricey side.
Simply due location, I wouldn't choose Idaho Springs, CO for lodging unless some specific reason you wish to do so.
Leadville, CO may offer you the least expensive lodging options in the area. Not entirely sure, but they may.
There are many lodging options within Summit County. Dillon, CO and Silverthorne, CO have more than a few.
Lodging in Breckenridge, CO would likely be some of the more expensive. However it is a lovely town with many cute Victorian boutiques and restaurants. All somewhat pricey, but you may feel worth it.
On the pricey side as well would be the
Keystone Lodge & Spa
Keystone Lodge & Spa - Hotel Highlights
A lovely complex within a nice setting. Something like this a good choice if you are looking for more of a resort, and don't mind the cost. Lots of amenities on site, but for strolling through a proper downtown you'd have to make the relatively short trip to someplace such as Frisco or Breckenridge.
Good luck.