I'm not sure if you mean specific neighborhood in Park City, or which town, or even which state. However, let me try to take a shot at this.
In my geographic area (Northern Virginia), this is what I'd look for: I'd look for a stable neighborhood. That means I'd try to avoid ones in which many/most of the homes had been sold/bought in 2005 or 2006. Around here, the greater the percentage of homes that changed hands in 2005-2006 (Woodbridge, Manassas, areas of Reston), the higher the foreclosure rate. That's driving prices way down. I'd look for communities with a more even purchase/sale date range. That indicates stability, and that suggests that many of the homeowners have equity in their homes.
I'd look for areas that are selling in fewer days on market. That indicates more demand, relative to supply. In today's market, around here, 30 DOM is very good; 180 DOM is not so good.
I'd look for areas near stable employers, or areas in which many people work for stable employers. Around the DC area, for example, there are communities in which lots of government workers live. The government is a very stable employer, so the people living there aren't likely to lose their jobs. On the other hand, I'd be cautious about areas where large numbers of people are self-employed, or employed in construction, for instance. Those jobs--and income--can vanish quickly.
Having said all that, buy where it works for you. You've got to like the neighborhood. You've got to be comfortable with the commute. And you've got to be able to afford a property you like. But, in today's market, you should be able to find both--something that works for you on a personal/financial level and something that is comparatively low risk/good reward potential.
Hope that helps.