I “second” what @gailcalled said about Mohonk Mountain House. great hiking or just chilling out inside the hotel (be sure to pay for the buffet lunch – you have to prepay but it’s great food, classy surroundings) and that gets you the entire day of grounds and indoor access. you could do that from the Bronx within one day.
other people suggested Boston – about 4 hours from Bronx but definitely a long weekend of culture. College town, museums, all good stuff. From there you can do a day trip to Cape Cod, which is scenic and maybe at this time of year it’s not that busy, but you can do some nature trails and stuff like that. Cape Cod is about an hour from Boston.
Washington DC – the great thing about Washington which not many people mention is that everything is free – your tax dollars at work. Museums like the Smithsonian and taking tours of government buildings – all free. It’s a little longer ride from the Bronx – probably 5 hours, so that’s definitely a long weekend kind of trip.