Pisa is a hard, winding, slippery climb. Please respect the age requirement. My kids went at 9 and did not climb the tower (climbed it at 13 yrs old, when we went back), but still enojed seeing it and seeing the rest of Pisa (we walked from train station-nice walk) and the Cathedral. Another good DIY with kids is to go to Lucca, then stop at Pisa on the way back. You can rent bikes in Lucca and bike the wall. There is a tower to climb in Lucca. It makes a really good DIY day. Be sure to get your train tickets online in advance. They are good for 4 hours. It saves A LOT of time, and likely enables you to make an earlier train.
My kids hardly remember Europe from 9 yrs old. The Med is very hot in Aug. and kids will be tired by 2pm and want to go back to the ship. Kids get tired of train/bus rides to places an consecutive days.
As long as you plan 1/2 days, lots of downtime and pool time, the Med will be fine. I might also suggest the Baltics, as long as you would be willing to leave kids in the kids' club for St. P, as it is too long a day for kids. We took our 9 yr olds and it was a long day for them. There are tons of fun, kid-friendly Baltic things to DIY. Norway is also a compromise between Alaska and Europe. We just did Norway and it would be kid-friendly, and it is a slow pace than the Med. and cooler. Copenhagen has a lot of great things to see. We saw no sea/wildlife on Norway cruise, if that matters. It rained 2/4 port stops.
Any choice will be fine, as you have the great DCL theming, dining, entertainment, and kids clubs. Just plan only 1/2 day trips, except maybe Rome, which could be a long day. Pisa, Lucca and Pompeii are easy and cheap DIY. Rome is a bit farther, but still doable DIY.