I think that when you are dealing with motorist traffic, shared paths with peds and bikes, crowded streets, and roads that are unpredictably chewed up and ridden with potholes that true interval training simply isn't possible. I have hit more potholes and crappy bumps that almost tossed me off my bike (would have, in fact, tossed me off my bike if I was going any faster) and if you don't have them memorized, they can sneak up on you FAST. I ride the belt parkway bike path and I can tell you this:

You already know about the sand and place where you have to walk your bike by Plumb Beach.
When going East from Flatbush to Crossbay, one would think that you could go all out, but there is a big chewed up road and bump section by the horse stables that will send you end over end off your bike if you hit it full speed. You have the little bridges over the water near Mill Basin, then Bergen Beach, then Canarsie, then Erskine, and they are all narrow and unsafe to go full speed.

You can open her up a little on the path between Ceasar's Bay (Bay Parkway and the Belt) and the five or six mile stretch to the exit at Owl's Head, but then you have kids running in the path, oblivious joggers with their earbuds making them oblivious to your presence, and so on and so forth, which will restrict you from true interval training.

Then you have the various greenways, like the Hudson River, which is a beautiful path but suffers the same fate as the one between Bay Parkway and Owl's Head. All the street bike lanes have dangers we all know about, such as sudden streetside car doors opening in your face, drivers completely ignoring the bike lanes, drivers going too fast, and a plethora of, you guessed it, potholes!

I can go on and on, and I know this post will be met with some resentment or anger, but I think true interval training on a bike in this city would mostly have to take place on a stationary bike. I just think it is way too dangerous to be opening it up and pedaling so hard that you could be seriously injured.

On the belt path at Bay Parkway, I will try to average about 18ish milers pee hour and even go more for short bursts IF there are very few people on the path and I can see far enough ahead, but that's about it. Same for various Greenway segments. And honestly, with motorists often driving erratic and unpredictably combined with the myriad of potholes and big bumps that could make you fly over your handlebars if you hit them at more then 15 miles per hour, do you really want to play with your life like that? I can't even begin to imagine doing 20+ miles per hour on the streets OR paths of NY City.

Just waaaaaay too dangerous. One mistake, either by you or a motorist, and you could be toast!

Edit: Here are my sort of loosely thought out speed rules for myself:

On a straight up empty bike path in good repair, with no people on it or almost deserted, I will go faster than other situations, but still won't force myself past 18 MPH average sustained speeds> I will allow myself about 20+ a little for very short bursts. This is in case unexpected potholes, bumps, chewed up road that a tire can "catch" in, and people running out in front of me.

On paths a little more crowded but not too bad, I shoot for around 15-16 MPH, giving me plenty of reaction time for unexpected and potentially dangerous road flaws such as holes, etc and also possible pedestrians on the path.

Dedicated bike paths on streets with traffic. I will go at most 15 MPH, but try to stay around 13ish or 14ish depending on road conditions and the aggressiveness of motorists on the road.

Share bike/motorist lanes I will try to stay around 13 to 14 MPH to allow some margin of error for motorists making overly aggressive or just stupid moves, as well as, of course, potholes.

On the street where there is no dedicated bike lane, I will shoot for between 12+ and 14+ and rarely if ever go faster. If I do, it would have to be a very deserted and newly paved blacktop and not for very long. Usually I am closer to 12 MPH OR LESS on streets that have a lot of motorists but that are moving fast, in other words where traffic isn't so intense that it is actually slowing me down and I am basically limiting my own speed not having it limited for me.