The cruise If it is a clear sunny September day there is some chance that being in that glass boat will be a bit like being in a greenhouse and you get steamed. I took a day trip one time and that was the result but can’t remember the month. Most of what you can see in the daytime from the boat you can see in the daytime from the trams. Or if you want there are some very affordable government run (BKK) river boats you can take during the day. The view of the buildings from the river at night though is a wonderful thing. I would do the well after sunset cruise. It’s never necessary to book tickets in advance. Well, not until you get to town and find out something big was going on in town that you didn’t know about, and the ship is sold out.
The Danube Bend towns to visit depend on you, how you want to travel and how much energy you have and how long a day trip you want vs how much more there is to see in Budapest.
I did all three with a private guide 23 years ago. It took over 12 hours, didn’t get to see enough of each and I was pooped out at the end. If I had to do it again, I would pick just one, but two would not be terrible.
The single best half day trip is Szentendre. You take the commuter train up. I would leave about 11:30. Takes about 45 minutes. That will cost you 450Ft extra if you have a TravelCard. Lots of nice places for lunch in Szentendre. Then you take 5pm the boat back; which is 4.500Ft. https://mahartpassnave.hu/hu/budapest-szentendre-budapest The website for the tickets is a nightmare. You can buy the ticket in Szentendre or at the Mahart office at the pier in Budapest. Or maybe you figure out the online ticket purchase. Do check the site though for sailing dates. Not every day and not all year. In the event that you cant do the boat, there is nothing wrong with the train. Here is a bit more: https://community.ricksteves.com/travel-forum/hungary/trip-report-day-1-833-szentendre-day-trip
If you did want to make a full day out of it, then you get an early start and first you do the open air ethnographic museum first: Szentendrei Szabadtéri Néprajzi Múzeum https://skanzen.hu/en then the town. https://maps.app.goo.gl/WxBW2mBNGDA98uR28
If you wanted to try and do two of the towns, the two easiest together I think are Visegrad and Szentendre. But that’s a train and a bus and a bit of a walk to reach the castle in Visegrad and then an hour bus to Szentendre. I think I would get on an organized tour for that. The castle isn’t terribly impressive. Pretty, yes. Sometimes they have medieval theme events, so they are worth it.
Esztergom, probably more interesting for me at least. But its best done alone if you are doing it solor, as its a train and a bus and will take you a few hours in each direction. But on a tour you might find one that hits Esztergom and one other.
For the organized tours and private transfers I would check GetYourGuide and Viator and then try and track down the vendor directly … or just use the platform. Or for a private transfer see what http://www.silverwings.hu/ can do for you. I've known the owner for at least 15 years. Good guy.
Another option is Győr and the Archabbey at Pannonhalma https://youtu.be/c7Q5Ap1qUj4?si=Vk46Tc8nnThhlaAV and https://pannonhalmifoapatsag.hu/ and https://youtu.be/kBYsexwEbPc?si=p-qBwvh0nppqpjWC . A good day trip and easy with a train up to Győr on a train from Keleti, then after seeing the old town and main square in Győr, a bus to the Archabbey (or a taxi).