Budapest December 4-9

Hi, joey. There is a ton of stuff to see and do in Budapest. It might depend on what you like - and weather. You could check out the Christmas markets, the ice skating rink in City Park, and ride the trams in the evenings. For museums, the House of Terror, Hospital in the Rock, the Pinball Museum, the Museum of Fine Art, the Hungarian House of Music, and the Museum of Ethnography (I haven’t been to the last one yet). Go up to Fisherman’s Bastion for views, tour the Dohany Synagogue, and stroll the Great Market Hall. Try a thermal bath (or two). Ride trams, eat cake, and sample lots of great restaurants. There’s music galore : from the opera house and Lizt Museum (you can also take a tour at both), churches, etc.

I didn’t know about the Beatles Museum. It looks small but fun - and not too far from other stuff in Eger (you might want an overnight).

If you read back through the Hungary forum, you will find a lot of great suggestions!

...and the Museum of Ethnography (I haven’t been to the last one yet)

And based on my experience, you haven't missed much. The building has an amazing exterior, and you may enjoy a stroll up to the top of the roof, but I found that many of the displays lacked focus within a rather confusing layout. The cafeteria that's located in the building's lobby would be a good spot for lunch or a quick warmup if you find yourself in the park on a cold day. There are other museums probably more worthy of a visit, and I found performances at the Budapest Opera and Liszt Academy to be quite enjoyable. And be sure to visit the ruin bar Szimpla Kert - you can go during the day for the farmer's market..

Is the Beatles Museum in Eger close to Budapest and worth while to
visit?

Budapest to Eger, train station to train station is right at 2 hours, so figure 3 hours hotel room to museum. Eger is a good overnight or two night stay, but given it sounds like you only have four full days in town, there are better day trips. Szentendre for their Christmas markets for example.

EDIT: I just noticed where you said you had 5 days, so, maybe its not unreasonable to run up to Eger for a night. If you are over 65 the train is only the cost of the seat reservation (about 3 euro).

Here are some posts that might help. If people think of others, if they add them here that might be useful for the OP

Vienna to Budapest by Train: https://community.ricksteves.com/travel-forum/hungary/vienna-to-budapest-by-train AND https://community.ricksteves.com/travel-forum/hungary/vienna-to-budapest-or-budapes-to-vienna-train-tickets-or-budpaest-elsewhere
Hotels: https://community.ricksteves.com/travel-forum/hungary/rs-forum-favorite-hotels-and-their-cost
Events through June: https://community.ricksteves.com/travel-forum/hungary/dec-thru-june-25
Events through October: https://community.ricksteves.com/travel-forum/hungary/list-of-budapest-events-july-through-october-25
Christmas Markets: https://community.ricksteves.com/travel-forum/hungary/the-christmas-markets-open-soon-in-budapest
Music Venues in Budapest: https://community.ricksteves.com/travel-forum/hungary/concerts-in-budapest
Budapest Guides: https://community.ricksteves.com/travel-forum/hungary/budapest-need-local-guide
Public Transportation Passes: https://community.ricksteves.com/travel-forum/hungary/authorizing-budapest-go-app
Using Money: https://community.ricksteves.com/travel-forum/hungary/money-in-budpest
Restaurants: https://community.ricksteves.com/travel-forum/hungary/restaurants-in-budapest-revisited
Mr E's notes: https://community.ricksteves.com/users/50322

The other advice that I can give is

1. Allow enough time to do it right. Budapest is a bit at the fringe of a lot of where people go in Europe, so return trips because you didnt stay long enough the first time are not as easy as in a city like Paris.
2. Its a large city so hotel location is important.
3. Public transportation is important because its a large city and because the trams down the streets lined with amazing old building is part of the charm of the city. So do get a proper transportation pass.
4. if you want to see a show or do a tour of the Parliament, book it as soon as tickets go on sale. Things do sell out and 15 November through 1 January is "High Season" in Budapest.
5. The Hungary Forum here has some amazing contributors with all sorts of travel style and interests, so ask questions.