New York City (& Surroundings)

Hi people I am planning a short trip to New York (& possibly the surrounding area). On top of my agenda is certainly the sightseeing, but am of course also for other activities (sporty or adventurous nature) to inspire. The whole trip will probably start from Munich and should take about 5-7 days. Regarding dates & accommodation I am flexible (although I prefer hostels). Outbound flight to New York, return flight either ex Washington or again from New York. Maybe you can find a travel buddy (or several) who has this area of the USA on his/her bucket list. I would be happy ;-) Questions always gladly.