To really get the most out of your vacation/holiday in the Rhine River Valley you need to be mobile and public transport simply doesn't conveniently give you access to all the Rhine River Valley has to offer.
I'm sure you also wish to discover some of the "off-the-tourist-track" gems.
If you don't have your own car, I really recommend you consider the option of renting one.
Unless you have some good reasons not to - and I can't think what they could be - it's far better to book the car you want before arriving.
If you don't it could happen (worst case scenario) there is no car available! or you have to settle for a car that doesn't fit the price/size/comfort niche you had in mind.
It's difficult to give advice concerning the type of car to rent as peoples' budgets,likes and needs vary so widely - we always go for cheap and small- one of the advantages when the kids no longer wish to go on holiday with their parents!! Bare in mind however that the car rental will be a relatively small part of the overall cost of the holiday and a few extra Euros spent for a larger car could enhance the quality of the holiday experience disproportionately.
Make sure before arriving that you have an international driving license or that your home license is valid in Germany.
Of course you'll want a car that's roadworthy and reliable but that can be taken for granted if you rent a car from any of the major car rental companies in Germany.(Avis,Herz)
You may well want to pick up your car at one of the 'local airports' - Frankfurt or Hahn and drop it off somewhere else but this will also present no trouble with the major rental companies.