Tony’s suggestion as to for the hop on and hop off bus is a very good option should you decide to use it. The only draw back to me is that you will get no feeling for the city with one of these tours, but again with limited time you can’t have it all.
Let me suggest another option that can easily be done with just a little homework. It will give you a feel for the hilly Buda side (Castle district) and some highlights of the Pest side (Andrasy Ave. & Hero’s Square and city park).
Although Budapest is a very lovely and easily walkable city with your limited amount of time you should probably avail yourself of its easy to use public transportation system. Buy yourselves a group travel card since it will be 3 of you and I am assuming you will all be staying together and not going your own separate ways …..here is the link you can also use its route planning tool if you are not comfortable using Google maps bkv.hu/en/…budapest_24_hour_group_travelcard
You will more than likely be coming into Budapest at Keleti rail station once you disembark you will want to get on the M2 red metro line and take it to Deák tér. Here is a link to a map of the metro system www.budapestinfo.org/budapest_metro_map.html
Now here you have a couple of options:
Option 1: Here you can catch the #16 bus up to the castle district. At Deák tér metro station follow the exit signs when you come out to the street turn to your right, and look for Erzebet Tér (Elizabeth Square) , it is the street you see as soon as you leave from the station. The bus stop is just in front of the Le Meridien and Kempinski Hotel which are located in front of Erzsebet Tér. You won't miss the hotels, so the bust stop is on the opposite side just in front of the hotels.
Option 2: Again make your way out the metro and this time just keep walking toward Vörösmarty tér here you will be in a big square where the famous Gerbeaud coffee house sits you can certainly stop now and have a coffee or a pastry or you can continue on through the square towards the river. Now make your way by foot over one of Budapest most famous landmarks the Chain bridge (Széchenyi lánchíd) and ride the funicular up to the castle district.
Once in the castle district you can see the castle walk a little ways and see the Fisherman’s bastion and St. Matthias church spend a couple of hours looking around it will also offer you some great photo opportunities of Parliament and the Danube as well as a wide sweeping panorama of Pest.
Now make your way back to Erzebet Tér (Elizabeth Square) this time I recommend you do use the #16 bus back you can catch it right by the Hilton hotel.
Now make your way back down into the metro and this time you want to get on the M1 yellow line the second oldest underground railway in the world and the first on the European mainland. Now travel toward the Opera stop which is where you will get off and exit. Once you come up to street level you will be on Andrassy Avenue (Andrássy út a Unesco world heritage site) and in front of the Budapest opera house another of the great Budapest landmarks continue walking east toward the Octogon intersection (I know a lot of people would not put this on a take a look at list but it is one of the more unique intersections you will ever see) Ok now you want to get back on the M1 metro line and make your way to Hero’s Square (Hősök tere) stop where you will get off. As you rise to street level you will be right in front of Hero’s square you can’t miss it make your way over and and directly behind it you will see the city park where Vajdahunyad Castle (Vajdahunyadvar) and Szechenyi bathouse are located and are definitely worth a look see.
Well now your time is almost up especially since I am sure you have stopped and has some lunch and rested a little during your whirl wind sightseeing day. From here you can make your way back to the train station either by walking which will take you about 30-35 minutes or by catching the #79 bus or by back tracking the M1 line to Deák Tér and changing to the M2 line taking you back to the station.
I know this is a lot to digest so if you have any questions feel free to ask most of us here on the forum are here to help our fellow travelers out when and if we can.
Additionally I can’t say it strongly enough that Budapest is not a city that expresses all it is and all its wonders in just a few short hours but this should give you some highlights.
Enjoy your trip I envy you, your day in Budapest but I also feel sorry that you will not have enough time to drink in all that it is.
Edited: 11:28 pm, April 11, 2013