I was able to go to the USS Arizona Memorial around 6:30 am one morning to raise flags over her for presentation to people that were retiring. This was in 2010 while I was stationed on Oahu.
At that hour it is eerily quite yet peaceful. Obviously not an opportunity open to everyone so I feel incredibly lucky.
On another occasion I did a Boy Scout sleep over on the USS Missouri. We were able to go to the bow and look at the Arizona at night. Simply incredible.
That entire place is a must see.
The USS Utah is located in around the corner of Ford Island from the Arizona. She was sank during the attack as well. There is a civilian baby in her hull. A Sailor had the remains of one of his twin daughters on board to scatter her ashes at sea when the attack occurred.
Funeral Held for Baby Entombed Within USS Utah
There are still 60 Sailors in the Utah hull. Because she is moored off Ford Island (a small island within Pearl Harbor) you typically need a DOD ID to get entrance and see the memorial.