Get a map
Okay, so your flight arrives at 3pm. Deplane, bags, taxi, drive, check-in, unpack, cleanup, etc: Its 5pm and you are in the Gellert Hotel in Buda. This is the same Gellert Hotel preferred by the likes of Heinrich Himmler and Oscar Schindler.
In front of your hotel you will find a tram stop. You want to get on the 47/49 Tram heading towards the river. This will take you into pest. Market Hall is on the right immediately after crossing the bridge (first tram stop). Most likely closed by the time you go by. On the left across from the market hall is the end of Vaci utca which was the main shopping street for communist leaders from all over the soviet empire. Here western goods could be purchased and here was the first McDonalds behind the iron curtain.
At the third stop get off and walk in the direction you were traveling on the tram. Look to your right until you spot the Great Synagogue and what was the entrance into the Jewish Deportation Ghetto during WWII. Again, its late and I think it will be closed. http://visitbudapest.travel/guide/budapest-attractions/great-synagogue/ Still a magnificent building.
Walk up the left hand side of the Synagogue, look through the fence, the tomb stones and the tree of life. Turn down the first street on your left (Rumbach Sebestyén utca) and you will go past the famous Rumbach utca synagogue. http://zsidonyarifesztival.hu/rumbach-utcai-zsinagoga/?lang=en
Continue walking and at the next intersecton take the pedestrian road to your right. You are in the Gozsdu Udvar (udvar = courtyard) http://visitbudapest.travel/local-secrets/gozsdu-courtyard/. You are about 15 minutes from dinner but you don’t want to eat before 7pm so pace yourself.
When you reach the first pedestrian intersection turn left and this will take you to Kiraly utca http://visitbudapest.travel/local-secrets/kiraly-street/ . Turn right on Kiraly utca and walk about two blocks to Kazinczy utca http://www.budapestbylocals.com/kazinczy-street.html Turn right on Kazinczy utca and ahead on the left is my current favorite restaurant in town, MACESZ HUSZAR http://visitbudapest.travel/budapest-restaurants/macesz-huszar/.
Okay, so now it is close to 8:30pm, but this is a wonderful safe town. Walk back to Kazinczy utca, then back to Kiraly utca, then turn right and go to the first street on the left; Vasvari Pal utca. On the corner is a little wine bar called Kadarka. Enjoy! But not too long.
Continue down Vasvari Pal utca until you reach Andrassy utca (you have to make one little jog to the right) http://visitbudapest.travel/guide/budapest-attractions/andrassy-avenue/ . In front of you is the Opera House. Walk to the right until you get to the Okatogon and enter the M1 Metro at that point so you get to see some of Andrassy ut. http://www.budapestbylocals.com/budapest-metro.html Enter the subway at the side of the street you are on and stay on the M1 to the Hosok tere stop (Heros’ Square) which is beautiful all lit up at night (as is all of Andrassy ut) http://visitbudapest.travel/guide/budapest-attractions/heroes-square/ and http://visitbudapest.travel/articles/andrassy-avenue-in-photos/
Now it get tricky. You want to be back at the 47/49 Tram by 11pm because I think it quits running sometime between 11 and 11:30. If you have time (15 minutes) you can take the M1 back down to the Oktogon stop (where you got on) and walk the lower half of Andrassy ut. If time is short then take the M1 two more stops which will put you at the end of Andrassy ut. The more of Andrassy ut you walk the better so get a map of the Metro line and figure 15 minutes from the Oktogon to the 47/49 tram and another 10 minutes more for each stop before the Oktogon. http://welovebudapest.com/budapest.and.hungary/sights.1/oktogon
At the end of Andrassy ut you will see the 47/49 tram to your left. Get on and ride till you see your hotel.
The next day, hire a guide. I’m tired.