I was looking up information on getting a permit to have a party in a New York City park and came across an entire section on having a wedding in one of the parks in any of the five boroughs. And while I found this link interesting, I just loved that there was a related link at the bottom of the page specifically for their picks on the most "picturesque" spots for a wedding.
The list of the most romantic parks in New York City for a wedding included multiple locations where—and I quote—you will often find New Yorkers hand-in-hand (or, sometimes, lip-to-lip).
Getting married in a park, whether in NYC or your hometown, is always a lovely setting but you need to remember that a Plan B in case of inclement weather is a must. Ask your local parks department what your options are if it rains. Some parks may have an indoor location you can use but others may not have another option for you. If they don't have a backup plan you'll have to arrange for one. Hopefully you won't have to use it!