I've lived in Denver for 4 years now and bought a house 2 years ago so let me see if I can help. First off, Denver is a big city. By every definition is doesn't fit that "small town feel." That being said, I think you'd love Golden or Longmont and maybe even Boulder. Other misconceptions people have about Denver.
1) Housing is expensive and getting more so every day. My 880 sq ft house on 1/10 of an acre is worth about $260k i.e. about 3x more than my friends with comparable houses in the midwest.
2) Denver isn't in the mountains. Expect to drive 30 minutes minimum to get to the foothills (Red Rocks / Golden / The Flatirons etc) and another 30 minutes minimum to get to Real mountains (Summit county/Nederland/Bailey) There are tons of running/biking trails within the city, a few nice rivers, and a couple state parks around reservoirs but it is not "The Mountains." It also has a number of golf courses down here but I don't golf and boo on you if you go to a course that irrigates. We don't have the water for that and it makes me sad that golf courses get a free pass on water use in people's minds.
3) The RTD light rail network follows the highways. I-25 South to Lincoln Ave, Santa Fe South to Mineral Ave, HW 6 West to the outskirts of Golden (no getting to downtown golden via light rail), and then next year they are opening I-70 East to the Airport and I-225 between I-70 and I-25. It is primarily designed to get you to downtown from a park and ride. There are a surprisingly few number of housing units near stations unfortunately. It also means that in almost all cases, if you have a car, it will be faster and cheaper (especially if you have more than one person in the car) to just use the Highway. That being said, I live 300 yards from a station and take the train downtown about 2x a month and use to commute via train. The system is in great shape and really nice to use, just not always the most effective.
4) The airport is 40 minutes away from downtown Denver even by car. Unless you live in Aurora (i.e. farther from the mountains) you'll live far from the airport.
5) We really don't have enough water. This year we got lucky but even the state government doesn't see how we can accommodate the expected growth between now and 2050 state wide from a water supply standpoint. Both the eastern and western slopes of the continental divide have said they expect the same water coming out of the Colorado River to be reserved for them. If you do move here, please be a responsible irrigator and let your grass go brown. No one will think less of you for letting your grass go brown.
Now that I've told you all the bad things about living here (you'll find most people from here try to encourage people not to come here b/c we're selfish that way :-) ) lets take a look at your wishlist:
(1) Mild climate with significant sun (ability to spend most days of the year outdoors). I am fine with some winter and some summer, just not the extremes. The front range will get a ton of sun, highs always below 105F, usually below 95F, very infrequent cold snaps where the high stays below 10 degrees F for a couple days, and winter storms that drop 8 inches of snow in 8 hours then it will all melt within 4 days.
(2) Access to good health care and health insurance programs/exchanges. Colorado has one of the few state run healthcare exchanges that are resounding successes. My wife (28 non-smoker) has a gold plan through Kaiser for somewhere around $250/month. Premiums have been fairly stable and there is an upstart insurance Co-Op that is shaking up prices and keeping things competitive.
(3) Access to the great outdoors -- for running, biking, walking, golfing See above, great trails in the city (the Cherry Creek trail, the Highline Canal trail, the South Platte River trail) even better stuff if you're willing to drive to the foothils.
(4) Urban amenities with a smaller town feel. I do not have an inherent dislike for suburbs, especially if well connected by public transport. We don't need to live in the middle of it all, but would like access to it. Urban areas with a strong "neighborhood ethic" could be appealing. This makes me think that Denver itself isn't where you should look. I think you'd like Golden especially, maybe Littleton, maybe Englewood, maybe Boulder, maybe Longmont
(5) Reasonable taxes for retirees. Decent cost of living. Other than housing, costs aren't that out of control. Milk is $1.99/gallon on sale. Gas today was $2.71/gallon. Property taxes are minuscule (I pay about $1700/year which is around 0.7% of appraised value). Beer is expensive b/c all you can get when you go out is (really good) craft beer but expect $9-$10 for a nice 6-pack and $4 for a happy hour beer out. Sales taxes in Denver are around 7% I think, outside city limits, its more like 4.5%
(6) Laid back attitude. Progressive values. Here is my scale of most liberal to most conservative. Boulder, Fort Collins, Denver, Golden, Morrison, Aurora, Parker, Castle Rock, Colorado Springs. Take your pick.
(7) Access to major airport. DIA is close (and getting closer with the new light rail line) but never as close as you want it to be.
Let me know if you have any other questions.