Outdoor Dinner Tonite in Williamsburg
This is definitely too late to be of any help for the OP, but I would strongly recommend that anyone looking for a serene, romantic garden in Williamsburg head over to A'shay on S. 4th between Roebling and Havemeyer.
The kitchen kicks out beautiful, savory French-Cajun specialties. I recently enjoyed the mussels in curry (make sure you can handle a good salty finish to each bite), and the mac & cheese was decadent, if a bit over-buttery. My dining companion had a nicely seasoned clam dish and crab cakes with the thinnest of breading and no discernible ingredient inside other than densely-packed fresh crabmeat. The garden is shockingly serene.
I'm heading there for brunch this weekend, and I can only hope they're able to maintain the sharp flavors and efficient service I received on my last visit. Be careful when you go - you might forget you're in Williamsburg, or New York for that matter.
Their seating's out front and no backyard, but Marlow & Sons is one of my favorite places to eat outdoors in Williamsburg. Or indoors, for that matter. It's probably closest to the JMZ, but the walk from the Bedford Ave L stop isn't too bad. (Plus, it's nice out for the walk.)
Santa Fe, on Union (Near the Lorimer L)
Dumonts, also on Union (Near Lorimer L)
Those are two quality, easy, reasonable (but not so reasonable that the food isn't well thought out) options. Both have backyards and are Veggie, Seafood friendly. Dumonts is a bit hipper and nicer, but I'm really digging Santa Fe lately--quiet, understated, great margaritas and friendly.