I believe someone here was asking about Szentendre. If you have 4 nights in Budapest, it’s not a bad idea at all. I would leave at 11:30 or Noon, have lunch in Szentendre and take the 5pm boat back
First, getting there, I think the train makes the most sense. To do that you will take the HEV Commuter train H5. You can use the Batthyány tér station which you can reach by the M2 (red) metro line or by the 19/41 Tram – or – you can board the H5 at the Margit híd, budai hídfő station which you can reach on the 4/6 Tram or the 19/41 Tram (trust me and use the Batthyány tér station)
Until you reach the Békásmegyer stop you are in the administrative jurisdiction of Budapest and your Budapest TravelCard will pay the fare. The fare from Békásmegyer to Szentendre will cost you another 310 forints. Buy the ticket before you get on at Batthyány tér. There are machines and there is a ticket window at the Batthyány tér stop.
From the train station in Szentendre, just follow everyone else to the old town. Not more than a 10 minute walk up-river (hint).
Coming back you will want to take the boat. Its easy to spot parked in front of the old district. Here is the website with the schedule and to buy the tickets: https://mahartpassnave.hu/en/timetable/danube-bend-with-hydrofoils/budapest-szentendre-budapest (I know the link has the word “hydrofoils” in it, but that’s from an age long gone … ignore it). Do board as early as possible so you can get a seat on the upper deck for the views. It is worth it.
Some years ago I had a special young lady visit so I decided to surprise her. I picked her up at the airport and we traveled straight to Szentendre (not much longer than going into town). After some hours in Szentendre we boarded the boat. Her first view ever of Budapest was rounding Margrit Island and seeing the Parliament building rise up out of the Danube before her. She still says it was one of the most incredible experiences of her life. Unfortunately, the moment last longer in her heart than …… anyway …… If that sort of thing interests you it does require a little coordination with the luggage, but I have the solution.