I have visited different parts of this wonderful country with my family by car for several years. I fly into a city hire a car for a week and tour. This country is huge. I suggest you could fly to New York City possibly and make this your hub as you will fly back from there. I am assuming that this trip is May on not winter.
Make a car trip south via New Jersey to Washington DC and back to your hub. The capital is a must. 4-5 days duration.
Then after a little sight seeing in NYC Drive north via Boston up through beautiful country to Montreal turn west to Toronto, Nigeria Falls, then east through New York State back to your hub. 7 days duration.
Take a flight west to possibly Sacramento hire another car and make a circle to Lake Tahoe it's beautiful for a few days then go south to Yosemite state park, fantastic drive and park. Drive south and west (1 day)to say Santa Barbara and then take the pacific highway north and drive to San Francisco (1 day) that is an on forgettable experience and stay in SF area for a while. Back to Sacramento and fly back to hub. 7 days duration.
You have time for one more trip and that is where I am now considering, upper north west to Portland Seattle area, or south west, Florida area so many choices.