They key is to leave your luggage out-of-sight. This is normally not a problem with sedans. In Europe, many rental cars are hatchbacks. Make sure you pull the hatch cover over your bags in that case.
I am typically not too concerned about parking my car in broad daylight. However, if you are unsure, use a secured garage.
Thanks Sam -- Where will I find "secured garages" in these towns?
In Spoleto at the end of Via Cacciatori delle Alpi. Take first exit from Rome, follow sign to train station bet turn right at the end of Viale Martiri della Resistenza, enter Piazza dell Vittoria (not Piazza Garibaldi) keeping the right lane. There is a small bar cafe on the right hand side.
Turn right just after that bar following Parking sign posted.
It is not just having the luggage out of sight after you have left the car. Make sure you have all you will need from the trunk before you get near the parking lot so you don't let observant people see that there is luggage in the trunk. If there are thieves around they will be looking for things like that.
When I've had to leave luggage in the car, I tried to find a parking space where I could back in against a wall or post or something where opening the trunk or hatch would make it a little more difficult for anyone trying to look in or open the back. It may not really make a difference, but I think if it looks to be more difficult someone would look for an easier target.
Also removing any "tourist" items from sight, like maps and GPS units would help lessen the target.
Thanks to those who responded.
The question I was really hoping to get answered is WHICH Hill Towns are Especially Problematic for Thefts from Cars
And are there SPECIFIC PLACES to park where those risks are minimized.
Umbria hasn't an alarrming rate of these crimes. A part of the advised already given, when your vehicle is in a parking on payment, there is no reason to keep worrying.
Our route has not been decided. It will be decided by where we can find safe parking. "To be blunt" it would ruin all of the fun to have our luggage stolen on the first day in Italy.
And "to be blunt" we dont expect guarantees in any part of our lives. But we do find some success in planning in advance to avoid problems.
If you can help with that, we would welcome your suggestions.