I will be flying LAX to IAD on July 8th one way, to catch an Int'l flight out of IAD at 11:00pm.

I was thinking of making use of the 8th by leaving on an early morning flight, do a stopover somewhere between LAX & IAD for upto 5-6 hours, then headout to IAD and arrive 2 - 2.5 hours before my Int'l flight at 11.

Its a family trip so I have 2 under 8 years kids and the wife. Any suggestions on cities to visit and routing to take.

Ideally I would like to spend no more the $225 per person, with just the 1 stop being in the city suggested.