Depending where you are going (check foreign office site) it can be perfectly safe to explore independently. The bonus of planned tours is you get a guide who speaks your language who generally shows you some highlights as well as your main destination. The cost of the tours will vary from around 40 euros for a couple of hours to 150 euros for a full day with lunch, it depends where you go, entry fees etc. On our Baltic cruise MSC ran shuttle busses to the main towns, that is the town where the port was, not the capital cities, the cost was 5 euros per person. We dared to try public (trains) transport in one city, it was great fun, we bought tickets from a machine which took a credit card so no cash required.
You have some time to decide which you want to do once on the ship, free guides and maps are available for each town on board.
If you give us some more info you will get good advise generally. Name the ports & we know where to start.