The Kempinski is a modern hotel in the heart of District V. Kempinski hotels are aways good. You did well with your cruise as Viking tends to use the Hilton in Buda which is a terrible choice for a short stay.
The bathouse is a great idea, maybe on your arrival day? The Basilica and the pedestrian area in front, also maybe on arrival day.? With out a lot of details of when you are coming and what time you have available, all I can do is throw out the standard one day tour.
I assume breakfast in the hotel. But if you want to start the day off Hungarian, then go out the back door of the hotel and you will be on Deak Ferenc utca. From there a short walk to Café Gerbeaud (opens at 9am). This is one of the classic turn of the last century coffee houses that Budapest is famous for. https://gerbeaud.hu/
The walk takes you in the right direction to head to the river and the 2 Tram. The 2 tram is often cited as being one of the best tram rides in Europe. Take it up river to the Parliament. If you book early enough you can do a tour. But you have to book way early. https://www.parlament.hu/en/web/visitors/purchasing-tickets While there see the Shoes on the Danube Memorial https://en.wikipedia.org/wiki/Shoes_on_the_Danube_Bank If you are interested in antique shops in basements, let me know.
Otherwise, while I hate back tracking, it’s the easiest for a short stay. So back on the 2 Tram in the direction from which you came. Stay on until it parks under a bridge. Then go up the stairs and in front of you about 100m up is the Great Market Hall. Be sure to visit the basement where the pickled-everything and the fish is to be found. The second floor is some pretty fair tourist markets, but I love the ground floor booths of vegetables, fruit, meats, sausages …. You name it.
If you are dying of hunger before or after the market you can eat in the market second floor or you can walk across the street to Vaci utca for some tourist grub; better yet behind the market is Borbíróság https://borbirosag.com/. I like it quite a bit. Mostly Hungarian flair.
After the market, you will board the 47 or 48 or 49 tram that stops in front of the market. You want to travel away from the river. You want to get off at the second stop (Astoria) and then walk up the tracks in the same direction and the Dohany utca (Great) Synagogue will be on your right; maybe 200m. It is Saturday so closed to tours. But the outside is beautiful and if you walk up the street on the left, you can see the Holocaust Tree of Life Memorial.
Then back on the tram in the same direction to the end stop. Then continue walking in the same direction until you reach the end of Andrassy ut. You need to walk the first third past the Hungarian State Opera (take the tour even). https://www.opera.hu/en/about-us/guided-tours/ I have had no problem buying them just prior. But …. Who knows. You can always buy the 4:30pm ticket in advance.
After the Opera continue walking up to an intersection called the Oktogon. Now what to do depends on the time and your energy. At the very least take the M1 metro one stop and then go up and walk one stop and repeat until you reach Heroes Square.
To get back to your hotel to get ready for dinner you take the M1 to Deak Ferenc ter. Then on the platform landing at one end you will see stairs going up. Go up those stairs and you will be in front of the Ritz hotel which is next door to yours.
Dinner reservation for Hungarian food and music: Rezkakas Bistro, which is very near your hotel. https://www.rezkakasbistro.hu/
After dinner, go to the river and look for Duna Corso. Hopefully they have a table outside that is open and you can enjoy the view.