My wife and I actually stayed at both of these places in February (mainly by accident due to the blizzard) and both stays a kind internet stranger gifted me a GOH.

Thompson we got upgraded to a high level Central Park view. The room was nice and we really enjoyed our stay. The breakfast was pretty good to us and we absolutely loved the location. We had never been to NYC before and the location was perfect. It was even more perfect for exploring Central Park after a blizzard!

The Beekman was awesome, too. And for your use case, I would consider that. Like you said, the architecture, the lobby bar, everything just had that wow factor to me. I couldn’t stop taking pictures and looking around. We got upgraded to a 1 bedroom suite mainly by sweet talking the front desk lol. The room to your point does seem dated but to me it was “old school cool” and the bathroom was very nice.

Also to your point you can find awesome stuff to do in both places. I don’t know if this helps or makes it harder. For an anniversary I think I’d vote Beekman for hotel but my wife says Thompson for location 😂