Alpine style refers to mountaineering in a self-sufficient manner, thereby carrying all of one's food, shelter, equipment, etc. as one climbs, as opposed to expedition style (or siege style) mountaineering which involves setting up a fixed line of stocked camps on the mountain which can be accessed at one's leisure. Additionally, for the purist, alpine style means the refusal of fixed ropes, high-altitude porters and the use of supplemental oxygen. There are plenty of adventures in the mountains of Italy to spend several days exploring.
The Alps have been the training grounds for many individuals aspiring to climb the worlds highest peaks. The highest peak is Mt Blanc but there are several other 4000 meter plus peaks to ascend. And many of the lower peaks might lack max elevation but technique difficulty makes them a challenge and nice addition to your 'tick list'.
Most routes in the Italian mountains are can be reached in just a few hours and few require more than a couple of days to complete. This makes your non climbing time a nice part of your road trip and if you are traveling with a non climber you can enjoy the both of each world.
This also means you do not have to carry as much gear as you would in more remote areas. However, this does not mean you can skip on safety. The weather can change quickly and with good attention to your surrounding and reviewing the many weather agencies forecast you can be better prepared for the day, but never take all this information as 100%, I have experienced many surprise weather days over the yeaR.