St. Goar or Boppard?

I think for your plans it makes more sense to stay in Boppard. On the day you arrive, after checking into your hotel, if you want to take a river cruise then take the train to either Bacharach or Bingen and do the cruise back to Boppard (that's the faster direction for the cruise), enjoy Boppard in the evening. Then on your full day, take the train to St Goar to see Rheinfels and then train to Braubach to see Marksburg - should be able to do both of them in the same day, or just pick one to explore. You'll still have late afternoon and evening to wander around Boppard again, it's a nice town. All of the towns are just a short train ride apart.

Can't help with Cochem or Burg Eltz, I've not been there.

You are packing a lot in. Problem: there are no lockers for your stuff at the Mosel stations while you do Eltz and Cochem on Thursday.
Boppard is a nice town - I stay there often - but it will be less convenient for your planned Rhine activities than St. Goar. Here's what I'd suggest.

"Tuesday, June 14 - arrive around noon, check into hotel, lunch and explore the town. May take a river cruise."

St. Goar, if you stay there - and I think you should - won't require a lot of exploration - only a few blocks long. I suggest you first visit Rheinfels (self-guided tour) that afternoon after lunch. Then take the 15:19 train south to Bingen (15:43) and catch the 16:30 cruise boat back to St. Goar (17:55.) Now take a stroll around town.

"Wednesday, June 15 - castles (Marksburg, Rheinfels?) and more touring"
(Rheinfels is done; Marksburg can better be done on Thursday - see below.)

You can do Cochem and Eltz on this day, but it will be a full day; return in the evening to St. Goar. "Train to Cochem to tour the town and see the falconry show, maybe Burg Eltz." I'd do Eltz first then the falconry show and Cochem so that Eltz doesn't close before you make it there.

"Thursday, June 16...(something..., then) Check into airport hotel late that evening after dinner in town."
This can be a relaxing "buffer" day. Let's say on Tuesday you didn't do the cruise for whatever reason (too tired? too hot in the afternoon?) Then you can leave your bags at your hotel, catch a train south to Bingen, and cruise back to St. Goar. Let's say you're back in St. Goar after the cruise at 12:00. Fetch your bags, use the FERRY to cross the river, walk a couple of blocks north to the St. Goarshausen train station, and catch a train to Braubach (about 20 minutes) for a tour of Marksburg. The TI office in Braubach will hold your bags for you. (Be sure to see the old town there too; maybe a meal on Market Square? )

Of course if you took your cruise on Tuesday you'll have even more time this day.... in the morning you could just take a train to Bacharach and/or Oberwesel (5-10 minutes) to check out these lovely towns. Then back to St. Goar for your bags, ferry, train to Braubach as above.

Once you're done with Braubach (don't forget your bags at the TI - fetch them before they close!) take the train to Koblenz (10 minutes.) In Koblenz you can catch the shuttle that goes to Hahn airport (20:00, 21:50.)

Thanks for the input! We will be coming from Munich to the area. I have been looking at the bahn.de web site for train travel. Can you provide the station names for the region? When I type in Sankt Goar, i get a list of hotels and other locations. What am I doing wrong? Also, is there any advantage in buying tickets in advance? Are there any discount fares that we should take advantage of? Am I correct to assume that river cruise tickets can be bought on a walk-up basis? No discounts ahead of time?

Can you provide the station names for the region? The station name is usually the name of the town with either an abbreviation for Hauptbahnhof (Hbf) or Bahnhof (Bhf). Without going on to Deutsche Bahn to verify, I'm going to assume that few of the small towns on the Rhine have a Hauptbahnhof, which is a term usually reserved for the main train station in cities. If you're seeing the names of hotels, these probably represent bus stops (Haltestelle in German).

Also, is there any advantage in buying tickets in advance? For long distance, high speed trains between major cities (Intercity Express, or ICE), yes, although it locks you in to riding a specific train. For regional trains, like you would use to explore the Rhine, no. Just buy them at the station as you need them, or take advantage of the various regional passes available.

Under most conditions, you don't need a car to reach Burg Eltz, although getting there requires an uphill hike. But as Russ noted, there isn't any place to store your luggage.

Cruise tickets: buy on site at the Bingen kiosk; show the train ticket you used to get there for a 20% discount: http://img.marcopolo.de/api/content/images/image/0/0/o/6o/t1024/u/photo-31344.jpg

St Goar (no period) is the station name.

"We will be coming from Munich to the area."

Munich station name: "Munich (München)"

You will probably want a pre-purchased saver fare ticket from DB for a good price. It's too early to price or purchase for your travel date. Using Tue 5/31 as a sample date I found fares for two adults... at 6:17, €48; at 7:15, €58; at 9:18, €48. You will find similar fares only IF YOU BOOK PROMPTLY WHEN TICKETS FIRST GO ON SALE (exactly 91 days in advance of your travel date.) If you wait and buy tickets on the day of travel the standard fare is over €200. (Saver fare tickets require you to commit to the travel schedule you choose at the time of purchase; refunds incur a penalty.)

Use the DB itinerary page below to enter your dates, travel time, destinations, # of adult travelers; when journey results appear, click on the white-on-red arrow at the left for details.

http://reiseauskunft.bahn.de/bin/query.exe/en

It is not clear where you are flying out from.

For your day trips along the Rhine and for Cochem and Eltz...

Tue: (If you cruise on this day...) €12.40 for two, St. Goar to Bingen, for a normal ticket, buy at St. Goar station.

Wed: VRM mini-group ticket, a day pass which covers you both (€22.10, valid after 9 am.) Buy it from a ticket machine in St. Goar on Wednesday morning. This gets you to Moselkern (for Burg Eltz hike) and then to Cochem and back to St. Goar, all on regional trains.

Thu: If you are cruising on this day: Rheinland-Pfalz ticket, a day pass at €29/2, valid after 9 am. (This day pass covers a larger area and gets you to Bingen; the VRM pass above does not.) Buy it from a ticket machine in St. Goar. If not cruising today, you can buy the cheaper VRM mini-group ticket again for the trip to Marksburg directly from St. Goar (ferry to St. Goarshausen is covered by this pass, train from there to Braubach as well. Depending on the airport you are using, you can use the VRM or the R-P ticket to leave Braubach (after your Marksburg tour) for at least for part of the trip. You'll have to state your airport for better advice.

If you only want to travel to Bacharach and Oberwesel this day, use the ticket machine again and just buy a normal DB ticket (€7.60/2 each way) for St. Goar - Bacharach. You can stop over in Oberwesel as you please with this ticket.

Here's a terrific page for Hiking to Burg Eltz from Moselkern

Thanks! We are flying out of Frankfurt Hahn airport.