If you walk west from Penn Station, you can then walk north along the Hudson River Esplanade past the Intrepid and as far as you want (I like going to the Cathedral of St. John the Divine) and then loop back.
Or go south along the high line and then you can go down to the financial district and up into the Lower East Side and Chinatown. Or walk up to Central Park and then go around then. You could also walk across the Brooklyn Bridge and see how far you get and take the subway back. Or go east, go by the United Nations, take the tram to Roosevelt Island, and walk around there.
Or take the 7 from Times Square to Jackson Heights, explore there a little, walk east into Flushing (normally I would say go to the Louis Armstrong House Museum on the way but it's closed Sundays), then loop down to Rego Park (if you want there's the Queens Botanical Garden, Museum, and Zoo on the way but with only 5 hours not sure you'd have enough time). Get a cheburek or two at Cheburechnaya (Bukharian Jewish food...basically kosher Central Asian empanadas) and either loop back to Jackson Heights or take a different subway to where you're going next. This one is less walking and more subway and eating, but the variety of communities you'd see would be very interesting and you'd get a sense of how more typical New Yorkers live!
Also if you really like walking in NYC, look for the Great Saunter in May. It's a 50k circumnavigation of Manhattan in a single day!
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