We just got back from a trip that included Budapest and had a wonderful time! It is really a beautiful city!
We only went out of town for a trip to the Hapsburg estate at Godollo (about an hour total from the city center by train) which we enjoyed but we didn't go to the places you list, we didn't drive, and I don't drink so I can't comment on any of those things!
We visited most of the well known sites (Parliament (great tour), Sts Matthias and Istvan Churches, Szechenyi Baths, Opera House) But a few things outside of that list that stood out for us are:
We started the first night with a Legenda dinner cruse and were very pleased. The food was good (my teen daughter ordered the vegetarian risotto and it was delicious) and seeing the buildings on the water at sunset was a glorious way to start a visit to Budapest.
My understanding is that the Alexandra Bookstore Café is still closed buy may reopen under new ownership? We did have a dinner at the gorgeous Belle Epoch New York Café and it was great memory. Food was fine, desserts were excellent, and to sit in the lavish building listing to alternating live piano music and a string quartet was unforgettable.
As far as history goes, Budapest has a complex history and seems to face it with fairly clear eyes. The "Shoes on the Danube" and Imre Nagy monuments, in particular were very moving. The "House of Terror" museum was not "fun" but did a very good and comprehensive job detailing the Nazi and Communist past in Hungary. My mother hated it but my daughter and I found it an important visit and well worth our time.
For architecture and somewhat quirky museum (but not that quirky) I highly recommend a visit to the Museum of Applied Arts. It's a stunning Art Deco building in a "Moorish" style. We went for the architecture but also found the permanent exhibits interesting, so it was a win on all counts.
Hopefully others will weigh in with their experiences, too. I really loved Budapest. It's a great city to just walk around in and lots of good things to do while there. We also found that just about everyone speaks English which was convenient--I never needed to use the Hungarian phrases I had memorized (good because I'm sure my pronunciation was horrific!). Also, we never had a bad meal there which what surprising but terrific--even sandwiches from the coffee shop were amazing--so that was a nice surprise.
We stayed at Hotel Moments and it was clean, central, and nice rooms, plus the staff were friendly and helpful, plus breakfast was very nice. My understanding is it's a newer hotel which may explain why it doesn't come up much yet on this forum, but I recommend it highly (dinner at their Bistro Fine was also very nice, we sat outdoors and ate a delicious meal while listening to live acoustic music).
Wishing you a wonderful time in Budapest!