Stamford is a nice young city, but some people label it "manford" because there are a lot of guys. As you are married, not necessarily a bad thing, and to be honest, I don't believe it really.
It is pretty expensive living, but there are plenty of cheaper options within Stamford. The problem is the location because you have two children. South of the highway is cheaper, but not as safe. I have some friends that live there though and they live in a nice area, so there are some options there.
North Stamford is very nice, but this is the really expensive area. West Stamford is similar to south of the highway. If you are considering a neighboring town, don't go north of Norwalk as the commute to Stamford would be killer. I used to commute from Fairfield and it would take me an hour at the minimum for twenty miles. It is awful.
Start looking early and you should be able to find something, but do expect to spend a little more.