I wouldn't describe Ouray as desolate at all...not sure what view they were showing you. There are some businesses for sale and some empty storefronts as there are in most communities these days; but there's still plenty to do, IMO. Telluride's larger and more upscale, (and more expensive, in general) with a greater variety of lodging, shops and restaurants; you can hardly beat the scenery. If you can find something within your budget, it would be a great place to vacation! But Ouray would be, as well... it is also walkable, picturesque, historic, and scenic, plus it is generally more affordable & it has the hot springs. And it is a little better base, IMO, to visit Silverton, Durango, Montrose/Black Canyon (Montrose has a couple of nice golf courses if any of your party golf), Ridgway. The two towns have different "vibes."
There are some townhomes right by the river next to the pool and park, (some of them come with a couple of free pool passes) but you'd have to walk (or drive) past the pool and park to get downtown...maybe a half mile or so, still very convenient to town and really convenient to the pool and park. There are some townhomes across the highway from the pool on the east side of the highway...I don't know if they are vacation rentals, but if they are, don't rent those, because they are literally right on the highway at the entrance to town.
Most of the hotels/motels are very convenient to downtown. A few have access to the same hot spring that fills the town pool. One of the neat things about the Ouray spring is that the water is odorless.
The Box Canyon Lodge has an apartment with full kitchen, plus a couple of junior suites, plus hotel rooms. They are one of the hotels in town that is located near the source of the historic hot spring water and they have their own wood hot tubs terraced on the hillside overlooking town, for exclusive use of guests. http://boxcanyonouray.com/rooms/
The Weisbaden is another hotel that has a variety of accommodations, and water rights to use the hot spring water.
wiesbadenhotsprings.com/accommodations.html
I have friends whose favorite place to stay is the Best Western Twin Peaks. It gets mixed reviews, but they have always found it clean and comfortable.
Here are a couple of agencies that handle vacation rentals, and of course there's VRBO, but with the variety of rooms that you need, VRBO might not be the best way to coordinate your locations.
ourayvacationrentals.net/Ouray_County_CO_lis…
http://alpenglow-properties.com/
ourayrealty.com/Real_Estate_and_Vacation_Ren…