NCL Cruise - Adriatic tour - shore excursions?

Question

We will be traveling by NCL - Gem to Izmir, Croatia, Greece and Italy. Please advise:
- the shore excursions seems very expensive
- is it wiser to travel on our own? how far it is safe? what are the advantages and disadvantages?
- do you have any suggestions?
- we had been to Athens and Venice already.
- are we allowed to stay in the ship if we doesn't want to take the shore excursions?
- do we have to carry our passport and other valuables where ever we go? is it safe? or safes are available in the ship? is it safe to leave our doc and money in the safe?

I appreciate your help and advise.