Where to go - I'm pretty open. I like history, arts, crafts and museums. I'm not a music/club person. I am tentatively looking at New York. I would love to see San Francisco but that's a heck of a plane ride. I am also thinking of flying to Albuquerque and see the four corners area, particularly Mesa Verde.
Since you want to see Mesa Verde, I am sure you would love it. I took my granddaughter a couple of years ago and went on the Cliff Palace Tour. You need a reservation for the ranger-led tours/hikes, but this time of year, it should not be a problem. We made ours the day before we went, but we were lucky to get in as only 2 spots were left. You could easily spend 3 days or more exploring Mesa Verde if you include one or two of the ranger-led tours/hikes. Or even it you don't.
Going out to Four Corners, be prepared to bring some spending money because there are lots of things for sale in an open-air market. It's a dusty drive out there, but very much worth the drive.
Where ever you fly to, if they have Fox Rental Cars, they have great deals. They are not at all airports, however, so not so easy to find.
New York City is a lot of fun, but you will surely spend a lot more money in New York than in New Mexico. Lodging and restaurants being the biggest expense. But in Manhatten, you don't need a car, so there is that. Of course, when you say New York, I don't know if you mean NYC or elsewhere in the state. There are plenty of places to go in the state where you would need a car.
If you go to Manhatten, I recommend visiting Central Park at least once or twice. The Metroplitan Museum is situated in the Park and you can easily spend the entire day there alone. The Guggenheim is in Manhatten, also worth the trip.
A boat out to Ellis Island and Liberty Island to see the Statue of Liberty is well worth it, but you need a reservation there as well. We did not walk up inside Lady Liberty (took too long to get around to making reservations), maybe someday.
The Nine Eleven Memorial is amazing just on the outside alone and well worth the trip. If you want to go into the Memorial Museum (run by NY state, not the NPS) be prepared to spend all day there and also be prepared to undergo some intense emotional responses. If you have young children, there is one room with a warning that it may be inappropriate for young children, and that is absolutely true. I barely managed it myself, and saw one boy of about 10 years old, lose his lunch. Very graphic in that room.
If you got to NYC, make sure to eat at least once at Ellen's Stardust Diner
. And if you are a Guy Fieri fan, he has a restaurant on 44th called Guy's American Kitchen
& Bar. If you like Sushi, Kodama Sushi
is the best place to go for good sushi and atmosphere.
And if at all possible see at least one show while you are there. You can get discount prices for select plays the day of the play by going to TKTS
Discount Booths downtown. Well worth the short wait in line for the discounts.
Just a few ideas for you based on my own travels.