I recently got curious as to which species of marine macroalgae I have observed so far in NYC. Here is an attempt at a list. Nearly everything is from Randall's Island; other species have their localities listed. Warning: some of these IDs are only guesswork:

GREEN ALGAE
Sea Lettuce -- Ulva latuca
Gut Weed -- Ulva intestinalis
Other Sea Lettuces -- Ulva spp
Bryopsis sp.

BROWN ALGAE
Rock Weed -- Fucus distichus
Bladder Wrack -- Fucus vesiculosus
Ribbon Weed -- Punctaria plantaginea [Soundview Park] but in Spring 2019 I found it at Randalls
?Ectocarpus siliculosus? -- or something similar-looking which grows attached to hard substrate.

RED ALGAE
Grinnell's Pink Leaf -- Grinnellia americana
Agard's Red Weed -- Agardiella subulata
Irish moss -- Chondrus crispus
False Irish moss, aka Turkish Washcloth -- Mastocarpus stellatus
Red Puff Balls -- Spermothamnion repens
Rusty Rock -- Hildenbrandia rubrum
Gracilaria ?vermiculata [this one from Fort Tilden]

Added in Jan 2019: Landlady's Wig -- Ahnfeltia plicata

I hope to add more to this list and/or refine it as I go along. Maybe I can add some nicer images too.