Budapest has some of the most efficient public transport we have ever experienced. Virtually the entire city is accessible by trains, trams, buses, metros, and boats. There is no need at all to take a taxi anywhere and the public transport is on time and inexpensive.
Our family of four ended up purchasing a one-month pass that covers all of the public transport within the city. The cost of this was approx. $45 CAD each (30 USD). The unfortunate part about that was that our children SHOULD have been about half of that price, however, since we homeschool and had no student ID cards for them, the ticket ladies REFUSED to sell us student tickets. Trust us when we tell you that we tried, we even had three amazing ladies from Budapest go out of their way to argue on our behalf! But alas, no discounted tickets. If we ever come back we will make up some fake student ID cards because paying an adult price for a child because of an arbitrary rule is just plain ridiculous.
Anyways, rant over. We really love the transport here, especially the above ground yellow trams. They are so cheerful and are a fantastic way to see the city. Indeed, many days we just hop on a tram without really knowing where we are heading. Then, when we see something that looks interesting, we hop off! We have found many a playground with this strategy!