Any 10 days in Czech republic would be awsome. The divorcee Slovakia is nice also.
The Tatra mts heavenly. Narrow roads the rule. Only driving experience but I would love to bike there. Drink some Budvar, have fun.
This is the easiest question ever - the Czech Greenways!! I cycled it this summer and it was fantastic. The cycling around Znjmno was GREAT, go south to Retz, Austria and enjoy some of the best cycling in Europe on the smoothest roads I've ever used.