I believe that Palma, on the same block as Home, also has an outdoor garden. August has an outdoor space, but I'm not sure if it's uncovered in the summer (there was a glass roof when I went a few weeks ago).
AOC on Bleecker (NOT AOC Bedford) also has an outdoor space, but food is mediocre.
Luxia, 315 W 48, has a serene and charming garden, really an overlooked gem in the theater district. Their frisee and gorgonzola salad is terrific and they have a nice hand with seafood. There is also a spicy red pepper penne that is REALLY zippy, a real favorite. It seems a world away from these mean streets.
And they make a nice martini.
How about Lattanzi on 46th between 8th and 9th? I was there last week for a long lunch, and I love that place. I think it's a cut above most of the neighborhood and it has 2 different outdoor spaces. The sauteed artichokes and the veal chop are spectacular, as is the bread basket.
Full disclosure: I know the owners, but I wouldn't recommend it if it wasn't really good.
Gascogne, the French bistro, on 8th Av., b/t 17th & 18th Sts., has very good food and a thoroughly charming back garden.
Gavroche, on 14th St., b/t 7th & 8th Avs., is another French bistro with very good food and a nice back garden though, in my opinion, not as quite as lovely as Gascogne's.
Note: Both website have photos of the gardens, so you can see for yourself.
Good luck with the date and Bon Appetit!