Cheap and near Minyan in NY area is almost impossible. The cheapest vacations is camping , you can get campsites for under $20 a day (I dont camp so I dont know exact amount), but Minyans are a problem.
There are very few vacation destinations near a Minyan, frum jews geenrally dont live in vacation destinations, even NYC which is a major tourist destination most of the minyans are in Brooklyn and not Manhattan (There are some Minyans in Manhattan)
You MIGHT find some minyans near Philly or Washington DC. But not in the tourist area. All the sites in Washtington DC are Free, but hotels cost a bit more