In the US, this is a pretty standard room layout.
One option you may consider is "adjoining rooms." You may be able to find out from individual hotels if they offer these (two separate rooms that both have inner-doors that connect to form a "suite" when needed). You will of course be paying for two rooms. In the US, unlike in other places I've been, you typically pay by the room and not by the number of occupants (up to a limit, of course).
Many larger hotels do offer adjoining rooms to a limited extent, and if you call and speak with them directly (vs. a chain's toll-free 800 number) they can usually accommodate such a request. For instance, the Wyndham hotel chain's Web site FAQ says, "We do have a limited number of connecting rooms and requests are taken at the point of reservation. However, due to the small number of connecting rooms, we cannot guarantee being able to honor the request."
There are some chains that offer "suites" at reasonable prices, but it's really luck of the draw on how these are configured, and there's no way (at least that I've found) to ensure you get one that separates sleeping spaces. For instance, DoubleTree has a few properties that are marketed as suites. The are configured with a sitting area (and a couch that folds out into a bed) just inside the door, a bedroom area to the back, and a washroom/hallway area separating the two. This provides a modicum of privacy without the cost of two separate rooms. Other hotels I've stayed at that offer "suites" just have a larger room with a larger sitting area in the same space.
Back to your original question... I found a site that offers an 'adjoining room search' called Raveable -- I've not used them before, so I can't vouch for their reliability/quality. But it is a start. Your best bet (unless someone else has any suggstions) would be to find hotels that you like via Kayak, Hotels.com, etc., and then call them directly (or even e-mail if you've got time), and inquire about availability of adjoining rooms and/or how their suites are configured.
Best of luck!