Edina is a great option, parts of the city have a fairly urban feel and parts are totally suburban. The NE part of the city, aka Morningside, used to be part of Minneapolis. Edina does live up to the stereotypes, very wealthy, very white, very good schools and sports, very well run city. Two country clubs take up about 1/4 of city, or so it feels. There is decent running in Edina. Not far from the Minneapolis Lakes.
Eden Prairie is basically totally suburban, has much more diversity than Edina, good schools, great sports. EP has neighborhoods built in the 70's, 1800sf houses, mature trees, pretty nice. There are also McMansions galore, built in the 90's and later. Parts of the city are fairly spaced out. The running is pretty good, lots of trails connecting neighborhoods, but not many opportunities for natural surfaces.
Wayzata is kind of a mix of the two, but has Lake Minnetonka. Lake Minnetonka is a massive lake that really influences the feel of that area. The lake has tons of bays that break things up into smaller pockets, pretty quaint feel in some areas. Not too diverse, a lot of $$ out there because of the lake, great schools and sports. To the west of the lake you get quite rural and beautiful.
Stillwater...if you want to have a sense of connection to the natural world, as you get living in mountains or on the coast, there is just a lot more topography and trees there. I don't know much about the school there, but your kids would be on a great teams.
All of these programs have really great sports and academics too, I know firsthand with the exception of Stillwater HS. I have no reason to think it is bad academically, just no personal experience.
The Three Rivers Park District offers some really amazing parks. I would love to live near one. You might check out their website to see the options.
Just thinking out loud, if you have decent finances, no commute.....one of the small neighborhoods surrounded by Lake Minnetonka would be a pretty great place to grow up. You could spend a day driving around the lake to seen how the feel changes between Beverly Hills and fairly basic homes. West of there are Carver Park and Gale Woods....two excellent places to run and ski. Check district maps, parts of Lake Minnetonka are in Wayzata schools, parts in Minnetonka, parts in Orono. Minnetonka is really good too.
Just a warning, Section 6AA and The Lake Conference (EP, Edina, Hopkins, Wayzata, Tonka) its is brutally competitive, probably the best Section in the country. That section CC meet is a blast to watch on a great course.
MN is a great place. If you're going outside the metro, Grand Marais is amazing, but sports and schools are probably not what the metro offers. Duluth is interesting too, great XC skiing on the "Iron Range."