How about spending 1 night in Venice? From Budapest there is a good chance. The irish low cost airline, Ryanair offers cheap flights to Venice Treviso Airport for 6199 HUF which is approximately 20 EUR per person each way. Dates: – 6th, 7th of June Booking on: http://www.ryanair.com
If you have an American Express debit card you are able to book this flight for only 6€ each way on http://www.edreams.pt
Google translate will help you to navigate on this webpage if you do not speak in portuguese. From Venice Treviso Airport you can take ACTT bus No. 6 to Treviso railway station. The ticket price is 1.2€ if you buy it in advance (2.5€ on board).
Bus schedules and route map: http://www.actt.it/trasportipubblici.php?page=1146239540
Trenitalia trains run frequently between Treviso and Venice S. Lucia station and the price is 2.9€ each way.
For more info, please visit: http://www.trenitalia.com/
Do not forget, when you fly Ryanair you have to check-in online before and print your boarding pass.
Have a good trip!