hi there,
Personally, Spring is a great time as it also coincides with the Budapest Spring Festival (March-April), which is one of the most
exciting annual events in Hungary.
The
Budapest festival is usually held the last two weeks of March and it's packed of spectacular cultural events, international and local performances, exciting exhibitions, and myriad conferences take first place this time of year.
If you travel during this time, you will learn a lot from the Hungarian culture and you'll also get best out of your holiday.
Hope this helps
Vacationbuddy