We also live in the Northeast, and also have kids who applied to schools out of state going as far as Colorado. With somewhat higher stats we got merit aid from most of the schools that our daughters applied to. However, we only got enough aid to get the total cost down to $30,000/year or less at in-state public universities, and at schools in Canada.
Given an EFC of ~$63k, and a budget of $20k, I am thinking that your least expensive options are likely to be in-state public universities. Most students stay in state for the simple reason that is what most of us can afford. Fortunately you have good public universities in Connecticut.