Are Aquincum Museum and Pál-völgyi-barlang/Szépvölgyi Cave worth a visit? Do they warrant some time or are they something that I can skip when I'm in Budapest next month?
The Aquincum museum in Obuda is "interesting". What is more fascinating is that the Romans made it that far east; you can see Aquincum on this map: https://www.worldhistory.org/img/c/p/1200x627/266.png.
The Old Square in Obuda is interesting too. https://www.google.com/maps/@47.541358,19.0453752,3a,75y,227.11h,74.33t/data=!3m6!1e1!3m4!1syfB2NTybsrrMQePqWqNpcQ!2e0!7i13312!8i6656?hl=en&authuser=0
And there is more than just Aquincum (in Pest as well): https://welovebudapest.com/en/toplist/roman-budapest-6-ancient-sites-in-our-modern-city
Never done the caves, but have come close a few times; sounds fascinating.
If you can get into the Hospital in the Rock, the first 2/3 of that is fascinating, but skip the Labyrinth if you come across that.