Since I had great luck with a similar question about train service from Prague to Frankfurt, I'll try again.
We'll be taking trains in June between the cities listed above, are there websites that can assist me with booking the trips?
Thanks.

You can search for trains on basically any European railway network's website for any train within Europe. To book them online would depend. For example, Austrian Rail's site www.oebb.at has a "ticket by mail" option, but it's in German only. Not sure if you can indeed have tickets sent to you from them. Maybe others can help you.

Or if you don't mind spending a little more, you can buy all the tickets via websites like www.raileurope.com. You can purchase tickets, including seat reservations from them Vienna - Budapest and Budapest - Prague.

If you are going other places check railsaver.com to see if a pass is a better option. If not you can purchase through rail europe or wait until you arrive and purchase them at the station. FYI - check the German website bahn.de for schedules. The trip from Budapest to Prague is quite long.

The "Europe East" pass may indeed make sense. It covers all 4 countries you'll go or pass through, plus Poland.

5 days in a month is US$158, through raileurope.com.

Thanks.
ttt

To rkkwan - Great suggestion on the East European Pass. Unfortunately, Germany is not listed as one of the countries in this program. I e-mailed Rail Europe, inquiring whether the Preague to Frankfurt trip would qualify since it originates in the Czech Republic, but the response was no...we would have to buy point to point tickets upon reaching the Czech border, for an additional $97 per person, 2nd class.
So, I guess we're back to trying to buy a ticket for each individual leg of the trip separately. We could purchase all through Rail Europe, however, the only leg that we can compare cost on at this time is the Prague to Frankfurt trip - throuh the bahn.de site, the cost would be approximately $58US per person, while through Rail Europe, it would be $107 per person - not really my idea of just a few dollars more.

Any thoughts on how "safe" it would be to just buy tickets as we go, at each location? Any other suggestions would be appreciated.

I think that www.railsaver.com could help you in your decisions, but I have never heard for sure, if all its data are completely valid for the countries in _central_ Europe covered by the "East Europe" Pass.

Best wishes,

Rex

I have also looked at the eastern european pass and agree that it does not work in Germany. The best information that I have seen regarding different railpasses and what is included is on Rick Steve's website but Railsaver.com will do the work for you if you plug in your destinations.

Thanks. Rex - I checked-out railsaver.com. Interesting...they quote a very competitive price for each trip you enter, but do not provide a schedule. Could this mean that one could get stuck on an overnight trip without wanting it, or one with 3 or 4 connections when there are non-stop or one-connection routes available?

Plus, when you click on one of the "Purchase Tickets" options, they simply direct you to buy them at the rail station in the originationg city. Maybe my trips are still too far in the future to purchase now? (Early to mid June)
I have e-mailed them with these questions, and will let everyone know what they say.

I wasn't aware of the railsaver site, thanks again.