I vote for 5 days in NYC (stay in Times Sq - central location, safe area, high energy) then take train to Washington DC for 5 nights. Arrange which city you go to first based on the Repubican Convention. Tons of great things to see and do in both cities with pretty countryside in between.

I travel to both coasts often for business and have the luxury of taking my family with me as often as schedules allow.
The overwhelming favorite destination for all is CA. There is just so much to do and it can be very inexpensive, much less expensive than NYC unless you are wanting to stay in 5 star hotels.
There are loads of hotels that offer free full breakfasts and afternoon cocktail receptions and many of these hotels also offer kitchens in the suites and free parking (not in the city of San Francisco) You can really save a great deal by utilizing this type of hotel and buying groceries at one of the big supermarkets. NYC has very few properties of this type and groceries are more expensive.
In addition, you can take a couple of days and go to VEGAS... or Reno, depending where you are.