Js, you are staying about 2 ½ minutes from my front door. You chose wisely. Do check with those two tour guides and see if one is available. Worst case you to to GetMyGuide or Viator and book something.
Not a hard city to see without a guide. Book your cruise with these guys: https://legenda.hu/en Unfortunately I will be too late to get tickets to the Opera, but you can do the tour (its across the street from your hotel). https://opera.jegy.hu/program/operatour-angoleng-i-106936
Without a guide I can give you pretty good directions to hit what you have time to hit. Its not hard. But when you get off the plane, in the arrivals hall, on your left you will see a BKK office, go in and get a 72 hour travel card. None of the fancy ones, the basic 72 Hour TravelCard for 5750 forints https://bkk.hu/en/tickets-and-passes/prices/72-hour-budapest-travelcard/ You can do this with the BudapestGO App as well but I think paper is easier and less for me to explain and maybe get wrong. I wont tell you about the taxis at the airport because I presume the W will pick you up? (or go outside to the curb and look to the left and see the taxi kiosk).
I can fill all of this in with detail if you want. Otherwise here is a broad plan.
Wednesday, not sure where you are coming from but you have a day and a half, so push through it and do Andrassy ut and the river cruise dinner. Then if you want to try some Hungarian wine after ….
Andrassy ut. Well out in front of your hotel is the Opera House. There is a 4:30 tour. Until 4:30 lets do a trip up Andrassy ut. The metro is in front of your hotel. Ride it to the Bajza utca metro stop, then do the walk back to the Opera house. It will take not less than 20 minutes and you want to be back by maybe 4:15. You could go all the way up to Hero’s Square (Hősök tere) but that’s a solid 35 minute walk back … so watch the time.
Do the river dinner cruise at 19:00. Give yourself 30 minutes for a scenic walk to the pier and 30 minutes early arrival or “I got a little lost on the way”. Or you could do a taxi but allow 45 minutes for that.
After the cruise the Kadarka Wine Bar is behind your hotel.
Thursday morning you walk across the street to Cork Breakfast and Wine and have breakfast.
Then walk down Andrassy ut. and board the tram that will take you to the Dohany utca Synagogue (Great Synagogue) and do the tour (opens at 10am) https://jewishtourhungary.com/en/free-tour
Back on the tram to the Central Market Hall https://piaconline.hu/en/central-market-hall/
Back on the tram and cross the river. I know a good Hungarian restaurant first stop across the bridge.
After lunch get on the tram that runs up the river bank until you reach the Chain Bridge then take the Funicular up to the castle district for the Fisherman’s Bastion and Mathias Church. Buy the ticket to get inside the church. Worth it.
Walk down the hill to the Chain Bridge and walk across it.
Take the tram to the Parliament building. I would say do the tour but doubt you can get tickets this late. But do visit the Shoes on the Danube. Now if you follow any of this and want to say thank you, I have a small favor to ask as the shoes. https://www.yadvashem.org/articles/general/shoes-on-the-danube-promenade.html
Enough trams. The weather is supposed to be good. Time to take a walk through a great park past amazing buildings, Ronald Reagan, to the Basilica.
Go inside and up to the tower of the Basilica. https://bazilikabudapest.hu/en/
Make the short walk to the end of Andrassy ut and you know where home is.
Dinner …. Well gypsy music? Better reserve now. Or just dang good food, better reserve now. Or something entirely local elite, better reserve now. Or …………….. send me an email address and I will send you a list. Many close to your hotel.
After dinner? One of three places for Hungarian wine.
