If you want a touring holiday, I'd personally say slow down and focus on one area, unless you have a specific reason to go to particular destinations. I do enjoy touring around as opposed to the "pick two cities approach" personally, so can see where you're coming from. You can get old cities, coast and mountains quite easily by staying in Slovenia and Croatia. Koper, Ljubljana, Bled, Bohinj, Rijeka and Krk... There's even a ferry between Venice and Pula to give you a head start and get you round the "taking the car abroad" worries.
Approach with insurance varies between the US and Europe. Typically, you get CDW with excess bundled into the price if you rent locally. If you rent from the US, the assumption is that you may have some kind of CDW cover. The rental company will need to ensure you have a "green card", as mentioned above. This may not be a physcial card, but it is to demonstrate that you have cover outside the car's country of registration.
Parking can be an issue, it varies too much from city to city to give a blanket approach. You may find an advantage in having a smaller car. One website that may help is
http://www.parkopedia.com/. Personally, I've had no problem driving and parking in some very dense, old cities, but it pays to research in advance. The cost can be significant in some areas.