The two "iconic" hikes in Telluride are Bear Creek Falls and Bridal Veil Falls. Neither is very difficult and both are close to town. I think Bear Creek was maybe 4.5 miles out and back, Bridal Veil Falls was a little shorter. I wouldn't miss either of those.

Not sure where you are staying in Telluride, but definitely take advantage of the free gondola that runs from sunup until maybe midnight or something. It connects the town with Mountain Village. We went back and forth a lot between the two places and the gondola is a slick way to do it.

We hiked the Perimeter Trail in Ouray. It's just as it's named - the trailhead is right in town and you hike around the town in a circle, never really that far from town. To be honest, this hike was just okay, especially compared to the Telluride hikes. If you want, you can hike to the "highlights" instead of hiking the full perimeter loop. If you are going to only hit the highlights, I would park and hike to Cascade Falls and then do the same to Box Canyon. I really thought the Box Canyon section was cool. We hiked this on a warmer day, so that could have influenced my opinion, but I probably don't need to hike the full perimeter hike again. You have some decent views from several spots along the way, but nothing compared to Telluride (IMHO).

Some of the restaurants that I remember:
Brown Dog Pizza - popular casual pizza place in Telluride that gets pretty busy. I enjoyed it a lot and would go back for sure.
Chop House Restaurant at New Sheridan - high end steakhouse in Telluride, really good food but pricey.
Uno Dos Tres - casual Mexican restaurant in Telluride with some unique tacos (it's an order individual tacos kinda place). We enjoyed the variety and different tacos.
Esperanza - another Mexican place in Telluride, more traditional sit down, nothing special and I wouldn't go back.

We enjoyed the hot springs in Ouray after hiking. I would do that again, although I think it would be more enjoyable in the evening or on a cooler day.