Even with your expanded budget you may want to give DC a hard look. DC vacations are a subsidized vacation -- most everything to do there has been paid for by your and mostly others' tax dollars. Because of this, your vacation dollars can go a lot further. This also helps control of hidden costs too.
You do not need to stay in Downtown DC to enjoy the sites -- hotels 20 minutes away in Virginia or Maryland will work just fine and are frequently filled by downtown DC-tourists. Just look for a hotel on the Metro (rail) system. This is the DC-area's subway, and it one of the cleaner, safer, and easier subway systems around. Also consider one of the Hop-on-Hop-off busses for the family.
When flying in to DC, aim for National Airport (DCA) as it could be $50 less to get to your hotel from there than coming in from Dulles (IAD). DC also has a great Uber infrastructure.
Wherever you go, I am sure it will be fun.