Both apartments and homes of all kinds to purchase. So, start your search with considerable homework and maybe a really good real estate agent. (beware of shysters--there are a lot of them too).
I lived for quite some time in Central Denver, within walking distance to Cheeseman Park, Congress Park and North Cherry Creek area (a pretty high-scale mall and shopping area, including a Whole Foods and close to downtown with all the cultural opportunities there. Expensive but I did like it while I was finishing a second graduate degree at CU-Health Sciences--now moved out east to Fitzsimmons.
Evergreen, Conifer, and Golden are doable foothill/mountain communities that many elect to live in (until the winter time commute overwhelms you) but it sure is gorgeous out there--Golden might be more practical.
Other areas can also be great, but commuting will be an issue--as in all big cities, but add in weather.
And, like many big cities now, it might be wise to check crime stats. Right now the major issue is car thefts. I love Denver, don't get me wrong, but not unexpectedly there are issues.