5 hours in Budapest between trains

My choice would be to hire a guide to pick me up and give me a 4 hour tour; returning me to the train station.

Second choice, and I am just guessing that you are changing at Keleti pályaudvar; is to walk to the front of the station and find the stairs that go down to the metro line. At the bottom of the stairs you can purchase tickets. You will need 10 tickets (total cost about $10.

You will then board the M3 (RED) Metro Line to Deak Fernec ter. The direction on the Metro Line will be towards Deli pu. Validate your first ticket in the orange box as you enter the metro station

Get off at Deak Fernec ter and walk to the Vorosmarty ter and then the Danube embankment.
Vorosmarty ter, Vaci utca, Danube Embankment, View of Buda Castle, .

The tram system is pretty sweet and it makes for a pretty impressive way to see the city.

Now board the No. 2 tram running left to right as you face the river. Validate your second ticket in the orange box.
one of the top scenic trams in Europe. Chain Bridge, view of Buda across the river, Buda Castle, etc; Parliament Building from the Pest Side

At the end of the tram line you walk across the boulevard street in front of you and board the 4/6 Tram. Don't forget to validate that ticket (3)

Get off at the first stop after crossing the river.
Margaret Island, and again the great views of the Parliament and the river and the castle on Buda Hill

Now you will board the 19/41 tram that runs back along the river front towards the Chain Bridge. Stay on it past the Chain Bridge to the Gellert Hotel (7 stops I believe). Again validate (4)
Vista views of Pest, Parliament, Chain Bridge,

At the Gellert Hotel you board the 47/49 Tram back to Deak Ferenc ter (ticket 5) and then back on the M3 Metro to Keleti Station (ticket 6).
Gellert Hotel of Eichmann and Schindler Fame, and one of the most opulent bath houses in Budapest, Great Market Hall, Great Synagogue, Museums

Okay, 4 extra tickets. The travel time will take maybe an hour and a half, so you will use those extra tickets for getting on and off and seeing things along the way.

Love the detail of your suggested "tour". Will save for future reference. Thanks you!!

I didn't say a lot about what you will see along the route, but it takes your through about 80% of the absolute best of Budapest.

" I am just guessing that you are changing at Keleti pályaudvar"

I haven't looked at the trains schedules, but be aware that there are three "main" train stations in Budapest. If you are not landing at Keleti, post which one you will be using, so James can give you directions from there. All of them are very accessible by trams and metro, but on such a short layover, you don't want to waste time figuring out the transit.

Thanks, James! We will be back for a week in March and will use your tram tour to get us started.

If you are staying in Budapest and have a full day to kill, it’s a great way to see the city. You can even split it into two days.

Then donate a second day to just the 4/6 and the M1 metro line.

Beginning at Deak Ferenc ter you take the M3 metro to Batthyány tér and then the 19/41Tram one stop to the Margaret Island Bridge (or walk, it’s not far). There you can get on the 4/6Tram and see some really amazing architecture and typical daily life from Buda to the Oktogon stop at Andrassy ut.; where you would get off and start walking up Andrassy ut. (mansions, embassies, great architecture, just a pretty place) towards Hero’s Square and City Park and the Bath House. It’s a long walk but the M1 runs right under the street so you can walk a stop, ride a stop, walk a stop, etc. Do the same to return to the Oktgon and then get back on the 4/6 to the Liszt Academy (very near), New York Palace, Museum of Applied Arts and the Corvin ter stop (lots of 1956 history) of the M3 metro that will take you back to Deak Ferenc ter. Great day trip with lots of potential for stops, food, tours, etc.

Which is why I sort of suggest staying close to Deak Ferenc ter (but outside the inner loop road) on near the M1 line.