There are several ways of getting around the Rhine Valley - train, boat/ship,bus,taxi and car. Lets consider these in turn.
The train service is good or perhaps "goodish" is a little bit more accurate but basically it just runs along the Rhine - you can quickly and easily get to any town on the Rhine but that's it.
A train trip along the Rhine does on the other hand enable you to relax ,take in the scenery and take photos at your leisure - not so easy if you're driving along the Rhine!
If however you want to go to any of the many interesting places in the Rhine Valley but not directly on the Rhine the train won't help you.
The trains from Rüdesheim to Koblenz run from around six o'clock in the morning to around ten o'clock at night in roughly half hour tact. The trip from Rüdeshaim to Koblenz takes about 1hr 45 mins. and costs around €12,00(one way)
The above times and prices serve as a rough guide as these are of course subject to changes by the railways.
I've included a link to the official Deutsche Bahn (German Railway) site but be warned - it is not all that easy to get around.
At the end of the page is a contact form - if you cannot find the information you are looking for, let me know and I'll do my best to find it for you.
The most delightful way of travelling up the Rhine is of course on one of the many small ships offering a Rhine cruise but this is normally by way of an outing rather than simply as a means of getting from A to B.
Leaving rail and river the next means of getting around is by road - bus, coach , taxi or car.
The bus services in the Rhine Valley are OK but no more. The service for places off the main route is definitely less than perfect and busses may only travel every two hours or so. I include a link to the site of the company servicing the Rhine Valley but finding your way around it may well be a challenge.
Coach trips - this is another way of travelling in the Rhine Valley but as with the Rhine cruises these are rather outings than just a means of getting from A to B.
Taxis will of course take you to where ever you wish to go BUT it might cost more than you expect - on the other hand if there are three or four of you then the convenience of the taxi as opposed to train and bus might make sense.
Tip : If you wish to go on a somewhat longer trip - say you are staying in Rüdesheim and wish to go the opera in Wiesbaden then before leaving agree a price with the taxi driver and this divided by three or four might not be all that much more than four times the train fare.
DON'T just get into the taxi and say Wiesbaden - that will be expensive!
We sometimes use this option if we are going to a party or festival where we all want to have a good time - the authorities here take drinking and driving very seriously - DON'T be caught over the limit (0,5 pro mille in this country) - it could ruin your holiday!!
And now we come to the last of the of the above options - by car. This is undoubtedly the best means of getting around -here as elsewhere. It opens many many interesting places that are simply not accessible by means of public transport or only with great inconvenience.
If you are driving to Germany from England (don't forget we drive on the other wrong?! side of the road) or from anywhere else in Europe then the problem is solved. If you are flying in then the options are - borrow, steal, buy or rent. I would advise against the first two - particularly the second.
Buying might make sense if you plan on an extended stay in the Rhine valley - three months or more. You might in fact end up selling the car for more than you paid for it!
Normally however the bureaucratic hurdles are not worth it for a shorter stay. In this case renting is the best option and if you are happy with a small non prestigious model it is not all that expensive.