Visit the town centre- parliament, Buda castle district, centrum etc.
Definitely visit some of the great hungarian spas...
I liked also Margita island and its park and the Jewish quater...
Also try visiting statue park with the socialistic realizm statues
If you have enough time visit also towns of Esztergom or Visegrád, they represent part of the Hungarian history... when it was really warm, we used to go to bath to Balaton, a lake some 100 km out of Budapest over 9 years ago
Wow. Must sees. Andrassy ut is a must see. Called the Champs Elysee of the East, it is a beautiful stroll and while walking it you'll see Hungarian luxury (oh wow, Louis Vuitton! Magyars do love their brands ;)), the gorgeous Opera (a must see), and it'll end, finally, at my favourite monument in Budapest, Heroes Square (my top must see). If you go behind Heroes Square, you'll enter Varosliget (city park, and also a must see), where you can visit Vajdahunyad Castle (gorgeous), check out the zoo, see one of Budapest's most famous -- and expensive -- restaurants, Gundel, the circus, and Szechenyi baths (MUST GO).
On either side of Heroes Square are the Museum of Fine Arts and Palace of Arts, both of which are pretty cool. You'll need to deffo see the Parliament, which is absolutely gorgeous, and next to Lanchid (the chain bridge), which at sunset, when it lights up, is breath taking. Crossing over into Buda, you have the Castle and Gellert Hill. The Castle has fantastic views from Fisherman's Bastion and Mattias Church is well worth a poke around. The statues and art of the castle are lovely. Gellert Hill is a nice hike that takes you to the liberty statue and also offers a stunning view of Pest below.
The island in nice weather is deffo good to see, but not a must see. It's mostly people enjoying their weekends outside and/or having a drink. Renting a bike for two on it is heaps of fun, though! The Jewish quarter is lovely and the Synogogue is the biggest in Europe, it's an incredible sight to behold. The Terror House, also on Andrassy, is my favourite museum and a definite must see for anyone who visits. Gerbeaud, the famous bakery, is worth every penny, and it'll put you on Vorosmarty Ter which back ends with tourist street, Vaci, at Vorosmarty Ter, there are often markets (depends when you come), and heaps of shopping. over 9 years ago
There are some stunning baths in Budapest - Here is a blog post from a friend of ours about them - http://www.pausethemoment.com/2011/08/04/best-baths-in-budapest about 8 years ago
Balaton Lake is my favourite! And when travelling with kids a must do activity.
Vesprem Zoo or Budapest Zoo both loads of fun and well kept
The Grand City Circus in the City Square is very much Cirque du Soleil this year and pretty awesome. The kids loved it!
http://tinyurl.com/3dzxxoj about 8 years ago
Def the terror museum. Also, the hospital in the rock on the Buda side is really neat. It is a hospital that was built completely underground in the communist times.
I loved the big market ( can't remember the name but it was designed by Eiffel) about 8 years ago