You're a little short on info here, such as what's your budget? Do you want a country club neighborhood? Are you planning to rent or buy? Denver has a fabulous system of parks, libraires and rec centers - things that are grossly underfunded or ignored in the transitory suburbs (I'm in Douglas County, no library funding for us thank you) I'm headed back to the city myself! Bonnie Brae is a great area, you might want to check out historic Congress Park. I was there for years, some great neighborhoods, you can be walking distance to City Park with the Zoo and Natural History Museum, another direction is the Botanic Gardens and Congress Park. Cherry Creek shopping is close at hand, there are some great neighborhood shopping areas and eateries. There are a couple of Catholic Churches and schools in the area as well as the Cathedral.
Like any urban area, things can vary widely in a fairly small area, Denver has some great schools such as Steck (my kids went there until we moved to Parker, in Denver we were in an elem school with 300 kids, in Parker over 1400) and Bromwell and some horrible schools - you have to do your homework. Denver has a lot of Catholic schools, each with it's own strengths or focus, you could contact the archdioces (used to be in Cherry Creek, might still be) and see what insight they can offer. Fewer than 1 out of 7 people here grew up here, so there has been a lot of change and growth. Many of us feel alomost lost in our hometown sometimes, talk to as many people as you can to get different insights.
Moving is a hassle but if you think this may be a long term move, you might want to rent for a few months and do a lot of exploring to find the area that is right for your lifestyle. Good Luck