Rhine valley/Mosel valley

We did a similar trip last year and did four nights on the Moselle staying in Bielstein in a great hotel with nice room with balcony and included traditional breakfast and they also served a good dinner and drinks outside,stayed three niights on the Rhine in a nice hotel in Bacharach with breakfst included and onsite parking.Without a car I would go for two bases to minimize travel from one valley to the other.There is a road that goes over the hill fromSt Goar to Brodenbach near Alken.Hope this helps you,PM me if you need hotel recommendations.
Mike

Beilstein is a tiny, tiny town and has no train station. Cochem is a good Mosel River base town... Lots of accommodations, dining choices, and a few diversions. If you want to visit Beilstein it's very easy to do from Cochem - take a river cruise one hour upstream.

Do you need two bases? One base will work pretty well if you stay in Boppard (a handsome town as well and a better base town than Bacharach on several grounds.) Boppard splits the distance between the extreme ends (Trier and Bingen) of the area you plan to visit and offers the widest choice of room and dining options.

http://home.kpn.nl/JLKampen1961/alb/Rome/Pauze%20in%20Boppard.jpg
http://www.jazclass.aust.com/blog/photos29/blog273.jpg
http://c8.alamy.com/comp/AYYGK6/framework-architecture-in-the-middle-rhine-valley-the-teehaeusje-little-AYYGK6.jpg
Gedeonseck, near top of Boppard's chairlift: http://pic.pimg.tw/samlucky5711/1379089584-1923285561.jpg?v=1379089585

If you intend to visit Trier from Bacharach, I would say "yes" - get a 2nd base town. It would take a minimum of 4.3 hours of round trip train time to do an outing to Trier.

Bacharach is a lovely town but despite Rick's affection for the place it comes with some drawbacks as a place to stay for several days. Train noise can be an issue. Restaurant choices are somewhat limited. Other towns like Boppard and St. Goar have ferries you can use to explore the other side of the river by train, but not Bacharach. Also, Bacharach usually works out as a less convenient place to end or start a scenic river cruise through the best segment of the Rhine River (somewhat easier from Boppard or St. Goar.) If you have a base in Boppard, you can still visit Bacharach very easily by train (or perhaps as a stopover by cruise boat between Bingen and Boppard.)

A good way to do wine is to stay with the winemaker. The Rademacher Inn is just one such choice in Cochem. It's near the town center and the station.

http://www.weingut-rademacher.de/en/

Russ - if we don't plan on visiting Trier is it realistic to do a day trip from St. Goar to towns such as Cochem and Bellstein. It looks like it would take around 90 minutes by train. The only reason we were considering 2 bases was to explore each area. Since we would like to go to wineries does it make sense to stay at the winery for 2 nights as our base in Mosel valley then head to st. Goar? Or is it possible to visit the wineries from St. Goar?

Between st. Goar and Boppard which would be a better home base it regards to places to stay, restaurants and traveling to Mosel valley?

Thanks for your help!

"Russ - if we don't plan on visiting Trier is it realistic to do a day trip from St. Goar to towns such as Cochem and Bellstein. It looks like it would take around 90 minutes by train."

Cochem, certainly - no problem. Either 75 minutes using the RE trains or 90 using the slower ones. Beilstein would require a bus or cruise boat connection. You hear a lot about Beilstein and it is cute. But I can't say you'll have the extra time for it - all depends on what you have in mind as you head up the Mosel. And I can't say whether a visit there justifies the additional time. Beilstein is only a few tour buses long. There are other fine towns on the Mosel as well. Winningen is a handsome wine town just outside Koblenz on the Mosel train route. It has 25 wineries, some of them very close in. Google Winningen and "Weingut."

"...we would like to go to wineries..."

Like Winningen, the other wine towns have wineries right in town. Boppard has a good number as well. St. Goar, fewer. Here's a list of Rhine wineries. No reason you cannot travel to the wine towns by train and visit wineries. However, not all are open for walk-in tasting experiences. You might contact the local tourist office to see which ones do that.

If you have just one day for the Mosel and are targeting Burg Eltz and Cochem, that alone will take all day (and a very full one indeed.)
Maybe if you take 2 separate day trips to the Mosel you'd have time for places like Beilstein and Winningen as well. Or maybe you just want to base in Cochem AND a Rhine town.

"Between st. Goar and Boppard which would be a better home base it regards to places to stay, restaurants and traveling to Mosel valley?"

Boppard, hands down.

https://upload.wikimedia.org/wikipedia/commons/9/97/Boppard_Weinhaus_R%C3%B6merburg.JPG
http://media-cdn.tripadvisor.com/media/photo-s/02/e0/0b/ce/severus-stuben.jpg (Severus Stuben)

But St. Goar isn't too far away and has a very scenic setting and a couple of OK places for meals as well. And the ferry. So you could dine in Boppard and return to your St. Goar hotel quite easily. Or from St. Goar you could ferry across and taste at St. Goarshausen's old-city-tower / wine museum.