A few weeks ago, I went on an 'edible plants' tour of the west side of Central Park, led by an ethnobotanist. I was familiar with some of the edibles, but these two were very pleasant surprises:
Chenopodium album, or lamb's quarters, or fat hen. This is a common weed and you can encounter it not just in the park, but growing out of tree pits on the sidewalk (not that I'd recommend you sample that particular specimen). The leaves were mildly bitter, like a mellow arugula. Really tasty.
Below is the flower bud of Commelina communis, or day-flower. The buds tasted very much like sugar-snap peas, though they were much smaller. This weed is also quite common and is easy to recognize due when you realize it's related to Tradescantia, a genus that includes the perennial spiderwort (T. virginiana) and the houseplant commonly referred to as wandering Jew (Tradescantia zebrina).
Like those other plants, Commelina will grow in sprawling heaps, the weight of the foliage too heavy to be supported by the fleshy stems. When the plant sends out a new branch, it looks distinctly like an elbow, with a knobby leaf indicating the point where the stem sends out new growth.