You posted under Germany but the only destinations you mention after landing are Prague and Amsterdam, so it sounds to me like this an inquiry about multi-country travel. Do you think you want to see some of Germany as well? I'll assume so.
"in our 20's, are okay with traveling cheap, and mostly looking for an interesting experience."
I think Prague is an interesting and lively place for almost any age group. Hank's suggestion - Würzburg - is a very good one if you're on your way to Prague. It's only 90 minutes or so from FRA airport (which has not just one but two train stations right by the terminal) by direct high-speed train. And it makes a good base town for short day trips by train to other places, some of Germany's best destinations, including...
Bamberg (university town, beer-lover's mecca, UNESCO World Heritage status)
Nuremberg
Rothenburg
Franconian Open-Air Museum in Bad Windsheim
Iphofen
Here is a train map of the above area (Bad Windsheim isn't shown but easy to reach - it's near Steinach.)
(Note that you might want to stay over in Nuremberg 1-2 nights as there's a lot to see there AND it's further along on the route to Prague than Würzburg. It would also be possible to make NUREMBERG your base town instead - day trips to the other places are easy from there too.)
After Prague you could head to Munich, and perhaps later to the Salzburg Austria and Berchtesgaden area, if there's time, before returning to FRA.
Transportation between these places is pretty straight forward and mostly direct. DB (German Railways) operates buses for the Nuremberg - Prague - Munich route at very cheap prices if you buy in advance. For your day trips around Würzburg (and the trip to Nuremberg if you stay there) the Bavaria Ticket (Bayern Ticket in German) is a day pass your group can buy day by day at the train station - no pre-booking necessary. Price is €37 - €12 each - for nearly unrestricted use of the local and regional trains.
Rail passes get a lot of bad press on this forum, and the reasons for this are often good. But that really depends a LOT on the itinerary you decide on. I rarely use rail passes, but I did two years ago when it became clear that the German Rail pass (which covers some foreign destinations too) would be to my advantage. Don't worry yet about the transportation yet - work on your itin. first and then find the transportation solutions.