Multi trip USA holiday where's best...and cheapest!

Duckyduck

If you like rides I'd highly recommend you take a trip to Six Flags Great Adventure while in New York. It's one of the biggest/best amusement parks in the US and has the tallest roller coaster in the world among many others. Six Flags parks are definitely more about the rides rather than theming/meeting characters, but I think they would appeal more to teenagers. NJ Transit run buses from the port authority bus terminal just beside Times Square in New York so it's a really easy trip. Six Flags New England is the park Jackieblack is mentioning, it's not as big or as close/ easy to get to with public transport, but still worth a visit. Dorney Park and Herseypark are also good parks a couple of hours from NYC, but again while possible to visit without a car, would really be much better to rent a car to visit these.

If you go to Disneyland in California, there's a public bus that goes literally from the entrance to Disneyland to Knotts Berry Farm a few miles away. Six Flags Magic Mountain is again excellent (though personally I like Great Adventure much more). From Anaheim (Disneyland) you can get a train/bus combo but it's a long journey, or an overpriced package type day trip, but really a car would be best for that one.

John259

This is a somewhat !!!!!! comment perhaps (or perhaps not?) but FWIW:

National parks are a lot less expensive than theme parks. There are about 58 national parks in the USA and here's a map showing where most of them are located:
http://www.terragalleria.com/parks/info/parks-map.gif

You don't have to do strenuous hikes to enjoy the national parks. You can drive round and see a lot, or do some short easy walks. They're totally suitable for families with young children, for example:
https://www.youtube.com/watch?v=24m6A4NhXUo
https://www.youtube.com/watch?v=xgo3gf9_q8Y

PeacefulWaters

I second building a trip around national parks.

So much better than theme park tat.

Indout96

Are you set on NY or just want a city break ?
Chicago is a cool place - you can stay by the airport cheaply but in very good hotels and get the train in to the city (about 25 mins) Lots to see and do.
and it has this : https://www.sixflags.com/greatamerica


Then on to LA for Beach / Parks (stay in Orange County not Hollywood) and maybe even drive out to Vegas and stay one night (about 4 hours drive if you avoid Friday)