Budapest is a great city and there are very important sightseeing places in Budapest, which cannot be missed. I would recommend the minimum of 2 days to see most of the important attractions in Budapest, if you squeeze out of the time. You will certainly need 3 days full to see major part of Budapest. There are also a lot of museums in Budapest to see and most museums take about 1-2 hrs to take a glimpse. If you wish to visit Lake Balaton (largest fresh water lake), apprx 1 hr from Budapest), i would suggest spending 1 more day extra to the tour itinerary.
Budapest has excellent public transport (tram, metro and bus) and you can certainly walk as well to cover major places in Budapest. I would recommend taking a budapest card which is one pass for all public transport and offers discounts in museums and restaurants. Deak Ferenc square is the main city centre and all the metro lines meet here. All the main tourist companies and hop on hopoff tours start from this junction. Inquire at the tourist information office near the McDonalds for any help you need. It is very near the metro.
Here are major places to visit in Budapest and i am summarizing below:
Buda Castle, Matthias church and Fishermans Bastion
The Buda castle, Matthias church and Fishermans bastion are very popular attractions on the Buda hill. You can walk across the towards the end of chain bridge and there is a funicular which takes you directly to castle hill. Be sure to see all these places and there are number of important museums out there like Hungarian History Museum, National gallery etc..
The Hungarian Parliament
The Hungarian Parliament is a majestic aesthetically crafted building and the front of the parliament is really beautiful. You cant miss the guided tour inside the parliament and it is a must see.
Heroes Square (Hosok Ter)
The Heroes Square is the place where Andrassy street ends and it is not far from Deak Ferenc square. There are important museums on the either side of the square and visiting them takes atleast 2-3 hrs. If you walk behind the heroes square, you can visit szechnyi thermal baths, the castle and a beautiful park. This is a very important monument and well worth spending your time visiting.
St. Stephens Basilica (Panoramic view)
The St.Stephens Basilica is one of the important tourist attraction and third highest church in Hungary. The sheer size of the basilica, its facade and bell towers is worth admiring. You can go on top of the tower through life and see the best panoramic views of Budapest and you cant certainly miss that.
The Margarit Island
The Margarit island, not far from Parliament is a long island completely a park. You can relax if you are a nature admirer of green vegetation. The park is very well maintained and is very big and certainly renting a cycle is very recommended to see the island. There is a bus which runs through the island and there are also hotels the end of the island.
Gellert Hill and Citadel
Gellert Hill is also a very important tourist attraction in Budapest. If you wish you can climb the hill starting from Gellert bath near Szabadsag and climb up. It might be tiring to reach Gellert but climbing up and down is a real fun part of exploring the hill.
Dohany Synagogue
The Chain Bridge (Szechenyi Hid)
Deak Ferenc Ter (Main city centre)
Vaci Street (shopping street)
The Vaci street is one of the main shopping and restaurant street in Budapest. It starts from Deak ferenc and is a very long street buzzing with tourists.
House of Terror Museum (Andrassy street)
The Terror museum on Andrassy avenue contains exhibits related to the fascist and communist dictatorial regimes in 20th century Hungary and is also a memorial. Tickets are not free but i think you can get discounts with budapest card. It is at walkable distance from opera.
The Hungarian State Opera
The State opera is one of the aesthetic beautiful buildings and must be visited atleast for a photo. Guided tours are available inside the opera and is worth visiting. For timings please the www.opera.hu website.
The Central Market Hall
The Central market hall is one of the biggest market halls in central europe. It attracts many tourists for its sheer size and there are hundreds of shops inside for shopping souvenirs, food items, hungarian delicacies at very reasonable prices. It is at Szabadsag bridge and it can be reached by taking a tram from Deak ferenc ter.
Castle of Vajdahunyad
The Vajdahunyad castle and entrance is not very far Heroes square and infact if you walk it is just behind it. This castle cannot be missed and especially a beautiful church inside it and you would love to take pictures of the castle and gardens. The castle is now Agriculture museum.
Nemetzi National Museum
The Hungarian national museum, is very near to Kalvin ter and a walkable distance from Deak Ferenc ter. It is a very big museum but it is worth visiting and having a glimpse of the monumental building.
Museum of Applied Arts
Lake Balaton: 1 day full tour
Lake Balaton is the largest fresh water lake in Central europe and is about 1 hr from Budapest and there are full day bus tour trips conducted by tourist companies which includes Herend porcelain visit, lunch and spending half a day at Balaton. During summer, over a million tourists visit Lake Balaton and is one of the main attractions in Hungary. Inquire about this at tourist information office in Budapest and they will book you with one of the companies. You can also take a trains which run from Deli Payaudvar station (Red line metro) to Lake Balaton, if you prefer. Very certainly, you will get to enjoy unique Lake Balaton and there are plenty of souvenir shops out there to shop. Be sure to add 1 more day to your trip itinerary, if you want to visit Lake Balaton.
Danube Night River Cruise
The cruise ride during Night is the best way to see Budapest with all bridges and parliament and castle lit up at night and it is so beautiful. You can get to catch a glimpse of both Buda and Pest on both sides when sailing. The cruise trip starts at night 20:00 and is about 2.5 hr trip including dinner. You have to get tickets at Budapest port or near Ersebet bridge (white bridge) on the river side, and there is a ticket counter to buy tickets.
River Ride Bus
The River ride bus is very unique and is main attraction in Budapest. The bus runs both on land and water and this way you get to see Budapest both on land and water.
References and Links
Tourist Information Office: http://tourinform.hu/english