I love La Vara (and her other places too) but I thought it skewed slightly to seafood when I’ve visited - easily verified by checking a current menu, though.
I don’t think Estela is under the tourist radar necessarily, but of course is excellent. Less lauded but I thought it was a wonderful meal (and setting) was Altro Paradiso in Soho (non touristy). He also has a new place in midtown but that will probably be a zoo.
Sounds slightly boring, but ABC kitchen has perfectly executed food in a lovely space.
Carbone would make for a special meal, but the large portions might limit variety if it’s just the two of you. Also reservations can be a pain.
Wayla on the LES is a delicious meal and their back garden is lovely and festive, but casual. The menu had a marginal seafood bent to the larger dishes when I went, but again that’s easily checked.
For Mexican, I still like Maya for a different style of food (and no tourists), also Toloache, but their ambience varies by location (food is very good at all of them last I ate there). Atla has fantastic modern mexican at a much lower price point than Cosme, but may be more casual than you are looking for. I’ve always enjoyed the food at Empellon too, the midtown location is fancier than the Taqueria.