If you will have grown fond of the Pacific Northwest you miss the ocean but I know EXACTLY where the office you'd be transfered to is and it is a pretty cushy gig.
USCG Marine Safety Unit Chicago, IL
$1600 will be stretched VERY VERY thin in Burr Ridge itself. There are many newer larger homes in town that get "Bill Gates" type price tags. There are a handful of more modest homes that you might be able to rent, but probably for considerably more than your budget. If your budget is capped and you are serious about a single family detached home your best bet might be to cast a wider net. Maybe as far east as Brookfield and as far west as Naperville. Between those extremes there are a whole bunch of choices to make. Bigger homes in more open areas, smaller homes in more traditionally laid out grids, a handleful of TOP NOTCH schools, some to avoid. Really needs to know more about how old kids are, what sorts of recreational things are important to you, how important to have neighbors that are from similar economic strata, racial mix...