hi there,
Hungary transportation include car, train, rail, bus and taxi. Although, I probably would not recommend car rental as finding parking can be a nightmare in budapest. Bus is your next best thing and will be considerably cheaper than
renting a car.
In fact, one of the best ways to see the beautiful city of
Budapest and many other towns and villages throughout the country is walking so consider that too.
If you eventually consider traveling to neighboring countries, I suggest the Eurail Pass, as it will give you great flexibility when traveling throughout Europe.
Hope this helps
Vacationbuddy