Staten Island is right next to Brooklyn and not to far from Lakewood or the Five Towns. There are many activities there that are inexpensive (once you cross the Verezzano for $16). Also Staten Island is not such a common dating spot so you are less likely to run into other daters.

Clove Lakes Park

1150 Clove Rd
Staten Island, NY 10301
 (718) 390-8000​

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Snug Harbor Botanical Gardens

1000 Richmond Terrace
Staten Island, NY 10301
 (718) 425-3504

Hours:
Sunday    10AM–5:45PM
Monday    Closed
Tuesday    10AM–5:45PM
 Wednesday10AM–5:45PM
Thursday10AM–5:45PM
Friday10AM–5:45PM
Saturday10AM–5:45PM

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