Belgium, Holland, Germany, Italy, Liechtenstein, Switzerland, France, Austria and Luxembourg - just have a high vis jacket with you and don't drink at all if you're not sure of their drink/drive limits.
Czech Rep, Slovakia, Hungary, Croatia, Slovenia - Although you might be concerned more about these countries, there is no need to be. They can't really be considered 'Eastern Europe' and all the negative connotations that comes with that. Your main problem will be that the roads are kind of shit so you want to stay on the main roads as much as problem.
Just secure your belongings, just as you do in dodgy parts of the UK. Dodgy police wont be an issue because you're not going far East enough. Just make sure your tires, tax, insurance and little things like that are all legal and you'll be fine