in New York? Is is good for a date? How far is it by subway from Say... Midtown? How much would a taxi be about... I am treating this new guy I'm seeing to night out, but I don't want it to be cheesey or a hassle.... what do you think? Cool or uncool?

I'm thinking you are talking about the one in the Bronx since I used to take my cousins there every year.

It is a rather cute exhibit where you have a bunch of different trees and plants you go through first. Then you see the exhibit with many miniature trains that go around New York City figures (Statue Of Liberty, Empire State Building, Chrysler Building, etc.). If your new guy is into trains then he would like this. The park itself is a nice walk around too (they also have a cart that goes around most of the gardens).

Afterwards, not too far away is Arthur Avenue (Little Italy of the Bronx). You can eat a nice Italian dinner there. I recommend Emilia's. Nice casual atmosphere with good food.

Via subway from midtown (don't know exactly where you are coming from in terms of east or west side) but if you are close to the "2" or "5" train, take one of them uptown (if on the "5", get out at the E. 180th Street station and change for the "2".) On the "2" get out at the Pelham Parkway station. Change for the BX12 bus westbound (the sign should read out 207th Street). You'll pass the Bronx Zoo on one side, the NY Botanical Garden is opposite of it (north). Get out at the Southern Blvd. bus stop (there is a McDonalds across the street). Walk up along the Botanical Garden....you know you are right when you see a parking garage across the street). The entrance is not that far up.

To get to Emilia's, take that same bus westbound (BX12) on Fordham Road and get out at Arthur Avenue (once the underground part of the road comes up) or you could even walk it if you want to Arthur Avenue. It's about a three block walk down to the heart of Arthur Avenue (E. 187th Street)...no buses go along Arthur Avenue. Emilia is on the right side of the street walking down Arthur Avenue past 187th Street. Link below....

There are botanical gardens in Bronx, Brooklyn, Queens, and Staten Island. Queens is small and, in your words, rather cheesy. Brooklyn's okay. Bronx is largest and Staten Island is nicest (with dozens of different rose varietals, among other things), with an interesting restaurant on weekends. But I wouldn't go to any of them until April, unless you like wandering in greenhouses.
Taxis to any of these from midtown is going to be expensive, >$30. The Brooklyn one would be the shortest trip, get off at Prospect Park. For the one on Staten Island, take a bus to Snug Harbor from the ferry.