Knowing what I know now about Budapest after 6 visits, this is what I do first upon arrival:
Head over to Margit sziget to see the storks as I like to visit in spring when they are nesting
Dinner is toltott kaposzta at Belvarosi Lugas Etterem near Szent Istvan's on Bajcsy-Zsilinszky ut
On my first visit to Budapest in 2014 I decided to conquer the metro and went a few stops to the Museum of Applied Arts (temporarily closed right now). Not a hugely important site to visit but it got me off to a good start. Then back to the Nagycsarnok to try langos at one of the upstairs food stalls. Neither were hugely important goals, I had several things on my agenda and they were easy, but it was the start of a very special relationship with Budapest and very fondly remembered.