Mediterranian cycling tour

I am planning to take my bike on a 5 or 6 week tour of the mediterranian in march, taking in Portugul, Spain, South of France, Italy, Croatia and Greece (although this is subject to change as i don't have any firm itinerary yet). As 6 weeks is not much time to get to all these places i had thought of catching trains between major towns/cities and using the bike for day rides and short passages (maybe 2 or 3 days) in between.

Fisrt of all, how easy/difficult is it taking a bike on trains in these coutries? I had though of getting a bag to put it in but would prefer to avoid this as it is one more thing to carry.

Seconly, does anyone have suggestions of places which are cool to visit by bike, or routes which are particularly interesting? I'm on a road bike, so tarmac or packed gravel only.

I rode the Berlin-Compenhagen trail in August las year, so have some experience of touring, but if anyone has other suggestions for this kind of trip (especiall with regard to keeping the weight down, i carried about 12kg last time) that would be much appreciated.