1. See the Funfair (Vidámpark)
It might not be interesting at all compared to Disneyland, but it has a certain post-Communist feeling. A unique experience for tourists and locals alike.
2. See the Circus
Only if you do not mind the smell and do not find circuses boring in general (as it is the same as any other Circus).
3. Visit the Zoo
The Zoo is a nice place to go with children in the summertime, and much more recommended than the Circus in the same time of the year (animals in a small building versus animals in open air).
4. Take a look at the Heroes' Square
The National Art Gallery is on one side and the Museum of Fine Art on the other. If you have an affinity for arts, the latter two are the places to go. Expect long queues.
5. Rent a boat or visit the icerink
Renting a boat in the summer, being a bit too sophisticated for the average citizen, lets you meet tourists like yourself. Sakting in the winter lets you mingle with the youth of Budapest. Try not to break a leg.
6. Visit the Castle of Vajdahunyad
This beautiful castle is right near the lake, housing the Museum of Agriculture. It is the right place for you if you are interested in relics like hoes from the 14th century.
7. Visit the Széchenyi Thermal Bath
The bath offers more or less the same services as all the other Baths in Budapest. Still, it is unique because of its turn-of-the-century architectural style.
8. Buy a souvenir or two opposite the Funfair
This is where the local commercial center is - yes, the stalls. It will make your kids and the seller happy.
9. Visit the Transport Museum
If you have any interest in vehicles, you will find this a joyful place. Don't be afraid to release your inner child and try out everything!
10. Take a walk in the City Park
The park is a great place to take a stroll. There is nothing to look at in particular, except a bunch of trees and green areas, but this is still the calmest, most pleasant place in the city.
At the same time, the Funfair does its best to renew. In the last decade, many internationally popular games were purchased, rented, or borrowed. These may be familiar and exciting for foreign visitors as well, even if they are bored with the traditional Roller Coaster (Hullámvasút), or the Scenic Railway (Szellemvasút), a true remainder of Socialism. The prices of the Funfair are more than acceptable, especially compared to foreign fairs. A multi-language prospectus is available at the entrance to help navigate among the games in the Park.
The Circus also emphasizes the maintaining of the traditions at the Hungarian Circus. Many artists trained in the Budapest Circus are now famous all over the world as performers as well as inventors of new attractions.
Nowadays, the Zoo has a more animal-centered policy than ever before. Most of the income is spent on improving the life conditions of the animals and the experience of the visitors. Lately, the Budapest Zoo managed to renovate and re-open the Palm House along with the Aquarium in the basement, and the Elephant House, attractions that no family should miss.
The Heroes Square is surrounded by the National Art Gallery on one side, and the Museum of Fine Art on the other, both offering various regular exhibitions as well as those of foreign museums.
The lake is the most well-known and perhaps the oldest ice rink in Budapest. For the past few years, however, they have set up a few others in other parts of the city. For example, there is one right in front of the Parliament. The other one is on a roof top by the Westend Shopping center.
Located near the lake in the City Park, Castle Vajdahunyad currently houses the Museum of Agriculture. Its exhibitions cover many fields of the history and development of Hungarian and European agriculture including domestic animals, plants, fishing, forestry, the history of wine, and many more.
The bath house is always full of people. In recent years, as the cost of the experience keeps escalating, there percentage of foreigners is also increasing. Actually, tickets seem to cost more than they actually do. There is a complicated system where you buy a ticket and then receive back some of it, depending on how much time you spent in the bath.
So this is a tradition in Budapest, just like renting a boat or skating on the ice rink. Buy something to see if you can become a little part of that tradition.