Thanks for all the feedback everyone.
We have booked our flights and hotels.
Fly in Budapest and 2 nights at the Boscolo.
Train to Vienna and 2 nights at the Marriott Vienna.
Train to Prague and 2 nights at the Hilton Prague.
Pretty much a day of traveling going and coming back.
Delta, KLM, and Air France. Train tickets via this site...the site says its too early to book them now for May, but we found non stop routes.
http://www.raileurope.com/index.html