I live in Parker and ride around the area all the time along with commuting from Parker to Aurora 2-3 times a week in summer/fall. Most of my rides I head west towards the Castle Pines area but I also do a loop that goes down to Castle Rock over to Franktown and then back to Parker via 83. I'm pretty comfortable around the area and I feel like there are plenty of alternatives when and if a particular route starts to get busier (i.e when a new development opens). Of course we have our fair share of a-holes like anywhere else but for the most part Parker is an active community and people expect to see bikes on the roads. That said I do avoid high traffic/use roads even if it adds to my mileage.

You can go Parker to Highlands Ranch utilizing MUP paths and never really see the road except for crossings. Susie Wargin from 9 news does a Highlands Ranch to Parker and back loop all the time, you can see her routes if you follow her on Strava. My proximity to the cherry creek trail (which begins almost all my rides) is one of my favorite parts of living in Parker.

Not sure where you'd be moving from but I love the area and think you would too.