There are many safe places to visit in Europe. I've been to Britian, Germany, France, Spain, Italy, Belgium, The Netherlands, Austria, Monaco, and the Czech Republic and I have never had any problems.
It isn't any different then visiting an area you are unfamiliar with in the US. If you are in the tourist places it is very unlikely any harm will come to you. If you are particularly concerned about safety I would recommend using a tour group or starting out with somewhere like Britian or Ireland where everything is in English so that you will feel more comfortable.