Hello from another 55410 mom!
My daughter (9) and I have lived in the Linden Hills neighborhood for about four years and I am still getting to know my way around Mpls! We rent a 1 bedroom condo, and I am aware that rental options are limited, depending on your budget. Linden Hills is one of the most expensive area in Mpls. We've managed it because we only need a small space. There are other nice neighborhoods surrounding here, that I would suggest looking into, also.
Have you found this website yet? http://www.ci.minneapolis.mn.us/neighborhoods/
It's been helpful for me when trying to understand the different neighborhoods in Mpls.
My daughter attends school in the suburb of Eagan, since her dad lives there, but my friends have good things to say about these schools: Lake Harriet upper/lower, Hale, Kenny, and Field. Two of my friends have kids on IEPs, one attends Kenny and the other Hale.
I'm a casual runner and normally run alone, but here is a site that lists several running clubs in MN: http://www.runningintheusa.com/Club/List.aspx?State=MN
Club Run Minneapolis is based right by Lake Calhoun, so in this area.
For summer camps, I would check with the YMCA and YWCA. My daughter has gone to YMCA Camp Kici Yapi for three years now and likes it a lot. It's a daycamp out in the suburb of Prior Lake. The YMCA provides bus pickup from several locations around Mpls. They also offer a Summer Power camp program onsite at local YMCAs. I'm not familiar with the YWCA programs.
If you don't mind driving farther, the MN Zoo in Apple Valley still has openings in their camp programs.
Leonardo's Basement: http://leonardosbasement.org/1history.php is right here in Mpls and offers cool classes/camps if your kids like building things.
The Bakken Museum is another cool place: http://www.thebakken.org/summer-science-day-camp/ But it looks like they are full.
Or the Science Museum in St. Paul: http://www.smm.org/classes
I haven't had to search for a babysitter, so I'm afraid I'm not help there.
Feel free to PM me if you have more questions!
S.