You didn’t say how you were going to get from the train station to your hotel. You could take the metro, but the station at Nyugati is a bit hard to find and you have to change at Deak Fernec ter. But if you are adventurous, then that’s the thing to do. Otherwise call a taxi. I like CityTaxi +36 1 211 1111 If you do take the metro, then purchase a 24 hour travel card from one of the machines at the metro station adjacent to Nyugati. https://bkk.hu/en/budapest-24-hour-travel-card/
If you took a taxi, first see if your front desk will sell you a couple of metro tickets. If they cant then you will have to go down to the Astoria metro station. So get your hand map and walk to the Astoria metro stop. Go down and find a machine and buy tickets if you didn’t get them from the front desk. On the street level you will find the 47/49 Tram. Hop on going left to right and stay on until the end stop. Get off and continue walking in the same direction 300 to 400 feet and you will find the end of Andrassy ut. At the corner of Andrassy ut you will see stairs down to the M1 Metro. Be sure to take the set of stairs to the metro stop before crossing the street. At the bottom you will find ticket machines. Buy a 24 hour TravelCard for 1,650 forints if you haven’t yet done it. Now you can travel for free.
Now you are going to get on the M1 metro line and ride it to the next to last stop, Széchenyi fürdő (bath). Go up the stairs and you are at the bath house. If you need flip flops or a towel, you can purchase both from the vendors under the trees. Now you have souvenirs.
I am going to guess you didn’t reach the bath house before 3pm and if you spend 2 hours now it is 5 pm. So walk through the park to Hero’s Square. Across the street from the square you will see the stairs back down to the M1. Depending on how tired you are you can make the 30 minute walk down Andrassy ut (it is a beautiful walk with some pretty interesting and beautiful architecture which includes embassies, magnificent old apartment blocks, and some pretty nice shopping at the lower end) or you can hop on and off the metro. Ride for one stop, get off and walk to the next stop, until you reach the lower end of Andrassy ut. Now its 6pm maybe. Return home to get ready for your cruise. It’s a pretty good walk from your hotel to the dock. I’ve take a couple and they are pretty okay. Personally with so little time in Budapest I wouldn’t be doing the cruise. But everyone is different. For instance, the Folk Dancing show mentioned in another post here bored the heck out of me. But that was over 10 years ago, maybe its better now.
Sorry, we didn’t make it to walking around the Parliament. How about tomorrow? AND, its really not a great evening strolling place….. My two favorite places would be the Danube Corso (the other side of the Chain Bridge from the Parliament) and the lower end of Andrassy ut, or Kiraly utca or the Godszu udvar.
The Duck Tour? If that is the bus they drive off into the Danube, that thing scares the heck out of me. No idea how you would get out of that thing when it rolls over.
The next day, go back to the 47/49 tram, this time in the opposite direction to the stop in front of the Market Hall (the stop before you cross the river) Go in and take a look, up stairs and downstairs. Very interesting. Then back out front, if you look towards the river you will see stairs going down. Take them. At the bottom you will find the famous No2 Metro (google it). Get on heading left to right. This will take you along the Danube to the Parliament Building and the Shoes on the Danube Memorial. On the way back get off at the first stop after the Chain Bridge and walk away from the river and you will find Vorosmarty ter. Show there till you are out of time…