Have you been to Chelsea's plant and flower district on 28th Street? Once in a blue moon I will visit them. Great variety but many of their plants are enormous! You might also try a visit to Chinatown, though I was a bit disappointed on a recent visit. Of course, there are always the big box stores. Unfortunately, the HD's and L's in suburbia have killed off smaller nurseries with...exotic stock and knowledge! If you are able to cross the river, MetroPlants in Fort Lee is pretty good.

i second flower district - on 28st bet 7 and 6 aves - but that is mostly house/office plants. cacti too and supplies.
but union sq market always has smth for herb/veggie and seasonal stuff.
bklyn bot garden has good corms/bulbs - they should have new stuff coming in the fall.
and also bronx bot garden - for potted perennials, but that's quite out of the way.

There is 'The Plant Shed' on West 96th Street in Manhattan.

There is the Brooklyn botanical Garden (have not been to that shop in years).

Then too, there are the big box stores (Home Depot, etc).

Unfortunately, the big box stores have resulted in the closure of many smaller, nurseries which have the expertise and variety unknown in larger chains.

When I lived in Queens, I used to go to Keil Brothers, but think they either closed or moved.

Interestingly, you posted about the Internet, because truth be told, I am doing a lot more Internet shopping for plants!

Maybe I am too late to give an answer now but may be helpful to OP for next year. My favorite garden stores on Log Island are:

GARDEN WORLD on Franklin Ave. in Franklin Square.

Atlantic Nursery & Garden Shop: 250 Atlantic Ave
Freeport, NY

Dee's Nursery and Florist Inc : 69 Atlantic Ave. Oceanside, New York