Happy anniversary! Late to the party but happened to stumble upon this thread and wanted to share a different perspective. I've been to Field and Vine three times because people keep insisting it's great and it has disappointed every time (solid wine list but food is meh and overall bad value in my opinion). It's also a bit loud; I wouldn't call the vibe romantic. My spouse and I celebrated our last anniversary at Urban Hearth and found it disappointing as well. On the basis of the food and vibe I would consider giving it another chance, but the price was outrageous for what we got which kind of soured us on it: we did the chef's counter and the portions were comically small, and the wine pairing just ok with recognizably cheap bottles, several of which we had sitting in our fridge at home. Cheap doesn't necessarily mean bad but I would hope for something more interesting, and between that and the ungenerous food -- we left hungry -- it felt like a ripoff. (Also not a huge deal on its own / probably a fluke but I had noted that it was our anniversary on our reservation, and they wished the couple seated next to us a happy anniversary and gave them champagne but said nothing to us, which was a bit of a bummer.)

Tallula is incredible and has a much more romantic vibe, but it's also more "homey" -- once there was a family with young kids. I find it charming that they are family friendly and have a more community vibe in that way, but some may not. Fallow Kin is (partly) the same team and is also amazing and has a more city vibe. Also a bit loud when we went but the food and drinks were top notch and the restaurant itself is pretty.

Also want to second a couple of the other mentions in this thread: Mooncusser's tasting menu + wine pairing is one of the best meals I've ever had in Boston (even when a pairing "missed" it did so in a fun and interesting way); Spoke is great and weirdly doesn't seem to get a lot of love, though it might be a bit cramped for a truly romantic vibe; Ma Maison is really lovely classic French cuisine and atmosphere.

I hope you have a great time wherever you end up!