When you are playing the tourist, it is nice to be on a mission, when you are not only moving about "because that is what you do" but when your movements have a purpose. Wiki loves Monuments can give you such a purpose.
The Wikimedia chapters of Europe are working together in one big photo competition to document the architectural heritage of Europe. Some countries like Belgium do not take part because there is no Belgium chapter and others like Italy do not take part because their laws assume copyright of Italian monuments.
This Belgium problem can be solved by its Wikimedians.
Italy deserves a quite different response. Just do not go. Ignoring Italy as a travel destination because your pictures are not yours to license is quite appropriate. A solution may be found in cooperation with the regional authorities in Italy; when this allows us to ignore such silly dictates from Rome, you will find it amazing what the Italian country side has to offer.