<Grinning> Redmond, almost by definition is family friendly. The (small) downtown area is eminently walkable, with a TON of interesting things to do (books/music/art/coffe/pubs/breakfasty places/firestations/parks etc), Redmond Town Center is a gianormous (for the area) mall, and then most of the rest of the city is bedroom community. Decent public schools ... some of the best in the Puget Sound ... but not up to California standards. Of course, kyaking, hiking, snow stuff in the winter and boating in the summer are all nearby, but that's this whole area ;)
For strollers
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1 - rear facing pram-type if your little one's still small enough...
2 - On the Eastside most of the sidewalks are in great shape, Seattle's are lousy. Rubber wheels are a must on the Seattle side of the lake unless you want to feel like you've got the woogidy wheeled shopping cart and have numb hands all the time.
3 - Something EASY. It's drizzly and damp here most of the time, so you don't want little cold droplets of water getting you on the small of your back and neck for ANY LONGER THEN ABSOLUTELY NECESSARY. (Best investment here, btw, is good quality, expensive raingear. The kind that breaths and feels like clothes instead of punishment. We don't get a lot of heat or snow, or even "Umbrella Worthy Rain" but boy...do we get the drizzles.)
On places to live
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I'll check with some friends who live over there currently for specific condo/townhomes communities in the area and repost...but...Has your husband checked with HR? I seem to recall the MS has (or should darn well have) relocation services available to you.
Great Pediatricians (okay, this wasn't on the list, but we commute from Seattle to Redmond to see our pediatrician, so I thought I'd toss it up here anyway)
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Pediatric Associates (of Redmond, 161st St is ours, but they're all reeeeaally good)
http://www.mypediatricassociates.com
They have 6 or 7 clinics on the Eastside, Weekend & Late Hours, & have Priviledges and rounds @ Children's Hospital. A VERY good group.
~Z.