Well, the answer can told by the respective embassies of Europe (The authentic one). According to me you do not require a visa if you intend to saty in Europe for 90 days. So better get it checked from any embassy whether they allow you or not. If one of the country allows, then you can visit whole Europe.
You will also have to apply for a passport. I got one 2 years ago and I remember they asked about felony convictions. You may want to start with the passport office.
If it is a short vacation and not a temporary residency, you shouldn't have a problem. Apply for a passport to one country and you will be fine everywhere else. Also, how long has it been since you were charged with the felony?