I reviewed Little Giant a couple of possts ago and that might be what you're looking for. Although I didn't sample the wine as we had their house cocktails, the list looked pretty good. Blue Owl might be another option. In the West Village consider Employees Only.
The best wine list I've ever experienced was at Babbo but the reservation difficulties are well documented and it's certaintly not "off the radar".
Not totally off the radar, but Country has been getting some excellent reviews. We haven't been yet, but we recently went to the Cafe at Country. To be honest, we didn't expect the food to be as delicious as it was. Bodes well, I think, for the upscale venue.
Forgetting about on or off the radar, if you haven't been to Eleven Madison Park since Chef Daniel Humm took over the kitchen, you should consider it. We have been there four times since his arrival, and his cuisine is outstanding! We had dinner again there this past weekend. Just when we think he can't possibly amaze us again, he outdoes himself with a fabulous duck for two -- a "Have we died and gone to heaven?" dish. Excellent wine list, perfect service, and a gorgeous space. Definitely a special occasion place.
Happy Birthday to your fiance and Bon Appetit!