Frankfurt > Rhine > Baden Baden ?? - Help me plan!

"Is it possible to dedicate only 2-3 days to the Rhine and then visit other cities such as Heidelberg or Baden Baden (or any others you recommend)?"

Sure. Heidelberg is OK for a day or so but not super high on my list; if you go there, you can supplement your stay with an outing to nearby Ladenburg and/or a journey up the Neckar River from H'berg to Bad Wimpfen. Heidelberg's "castle" is actually a more modern palace built on the ruins of a former castle; you probably want to save your castle time for the Rhine (Marksburg in Braubach, Rheinfels in St. Goar) and the nearby Mosel (Burg Eltz.) St. Goar or Boppard make for good train travel bases.

The train works just fine for all these destinations. Rail lines serve both sides of the Rhine and get you to Moselkern on the Mosel for Burg Eltz. The boat is a sightseeing experience - not transportation as such. Best cruise is from Bingen to St. Goar (1.5 hours.)

Baden-Baden isn't part of the Black Forest really and is mostly about spas, casinos, high-end shopping. It's also a poor base for train outings. If you want to do the Black Forest instead of Heidelberg, I'd suggest Gengenbach as a base town. You can get a guest card there for free train travel around the Black Forest during your stay (Konus card.)

Traveling by train should be fine. You could spend the first night in Frankfurt, exploring the city, then head out the next morning. You could actually use the boat for transportation. Take a train from Frankfurt to Ruedesheim where you can board one of the K-D boats going down river. St Goar would be a good spot to stay for a few days to explore the area. It is part of the VRM transit district and you can buy a daily mini-group ticket to give unlimited use of regional trains and buses for the day for 22.10 EUR

You can get train to Heidelberg from there in about 2 hours. I should mention that you can get to Frankfurt airport in less than one hour by train, so you really don't need to spend the last night in Frankfurt.

Train schedules and buy tickets: http://reiseauskunft.bahn.de/bin/query.exe/en?country=USA
K-D Line schedule: http://www.kdrhine.com/
Frankfurt Transit Network (schedule local trains to Ruedesheim): http://www.rmv.de/en/
Rhine-Mosel Transit District: http://www.vrminfo.de/en/home/

Sam writes, "You could actually use the boat for transportation. Take a train from Frankfurt to Ruedesheim where you can board one of the K-D boats going down river."

Sam's correct that this boat ride is easy to do as part of your transportation. And yes, you can board in Rüdesheim, which is right across the river from Bingen, rather than Bingen itself, if you wish - but the arrival of the train in Rüdesheim at :04 after every hour means you won't have time to get tickets and catch the KD boat leaving R'heim at :15 after (after the hours of 9, 10, and 11 that is.) So you must plan on about an hour of down time in R'heim. You'll find that there are more trains going to Bingen and arriving at more convenient times for boarding the KD boats. You can travel either to the Bingen Rhein Stadt station (which is closest to the KD dock) or the Bingen Rhein Hbf station (main station, a bit far if you're toting a bag.) Check the train schedules and plan accordingly before you head out.

KD fares: Bingen-St. Goar is €19.80 but show the train ticket you bought to reach Bingen (or R'heim) at the dock for a 20% discount and it's only about €16. (the KDRHINE site Sam provided sells a CRUISE PASS for €31 that you do NOT need to travel the above segment - so just buy the ticket at the dock in Bingen (or Rüdesheim.)

The VRM day pass Sam mentions is a good one for outings from St. Goar. Note that to the south, it's valid only to Oberwesel - you'd need to pay a few extra Euros for a point-to-point O'wesel - Bacharach ticket if you wish to travel the 5 minutes between Oberwesel and Bacharach. Also available is the Rheinland-Pfalz ticket - a day pass with wider coverage for €29/2. Buy it (or the VRM pass) from a ticket machine at the station.

You could easily spend a day or two in Frankfurt, then do a day trip to Heidelberg, then head up to the Rhine. If you want forests, the Taunus mountains border Frankfurt. Wiesbaden has luxurious spas as does Bad Homburg. You don't have to take time out of your very short vacation to go all the way to Baden-Baden.
Any of the towns along the Rhine are nice for overnight stays, Eltville, Bacharach, Boppard, Ober-Wesel or St. Goar. The ship ride going to Boppard or St. Goar from Rüdesheim, Eltiville or Assmanshausen will give you the best scenery. If you are taking the train from Frankfurt, don't get off at Rüdesheim unless you want to explore the town for an hour. Stay on until Assmanshausen and you then have plenty of time to catch the ship after you get off of the train. The ship goes from Rüdesheim across the river to Bingen, then back across the river to Assmanshausen. You don't miss any scenery at all doing it this way.