Moma is worth a visit, but for a more lively Art experience ánd for free, one should visit Chelsea. A colony of 400 Art Galleries, showing the best in contemporary art. Running straight through is the high line, a 1 mile long linear park, build on a former railroad-spur, worth the walk.

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This is very small and not much but if you're a fan it's nice to stop by and cherish this legend.

I often run to this place and I love this perspective on glittering Manhattan and the feeling of coolness in the air from being so close to the water. To sweat and breathe and see this view of New York gives me a sense of being in this great City.

This is a pro tip, but also a summer tip, take the ferry from Lower Manhattan to Rockaway and spent the day. The beach is great and the area is impossible to gasp that it's 30 min from Manhattan (without traffic) - Eat as many tacos you can, cause it's the best in the state of New York!