Right now, we are looking at London for NYE - there is an awesome
firework display.
As there is in many cities. While I'm no fireworks connoisseur, I'm not sure London can beat Edinburgh (or just Scotland in general) when it comes to celebrating the new year.
That being said, should we do Prague, Budapest or Berlin to pair? You
all just made it harder for us to pick :/ How should we split the
time?
There are several options, but I still stand by my recommendation to look at orthodox countries. Lviv can also be good choice, charming city in general but I don't know anything about Christmas there.
It is cheaper to fly into LHR on the 24th - So should we just go
straight to our next destination for 5 days & then make it back to
London 5 days before NYE?
The best way is usually to first decide where you want to go, then book a trip there. And booking a trip to London if you don't plan to go there sounds like a terrible idea. London is probably the worst city in Europe for transfers in my opinion. And the UK is one of the countries in Europe that shuts down the most over Christmas. So if you plan to self connect you might be really stuck if you miss your flight (as in, you might struggle to find open restaurants and a hotel to stay in). In addition, the number of flights to other destinations will be limited on the 24th.
If I where you I would do the following: Fly to where you want to spend Christmas (Tallinn, Lviv or somewhere else), after a few days there, fly to London (if you want to see London). If you arrive on the 27th, the city will have woken up again. Then on the 30th, take the train to Edinburgh for Hogmanay, fly home from Edinburgh. Hence, book an open jaw ticket to Tallinn (or Lviv or Prague or somewhere else) and home from Edinburgh. From Boston, my first choice of airline for this would be Lufthansa, maybe SAS or Austrian (depending a bit on where you want to go).
Regarding calendars, most countries in the world use the gregorian. But some orthodox churches still use the Julian, hence the celebrate Christmas in January. But not all, so make sure you check. The Finnish orthodox church e.g. celebrate Christmas in December.