Hi
We have 'done' Gibralter several times on cruises, never on the Disney ship though!!!
It really is a very small Island and very British - even down to the red phone box and post boxes!!! A little bit of the UK in foreign climes!!
I would certainly recommend doing your own thing. No waiting around for tour groups, you will have plenty of time to get back to the ship, you can actually see it from most parts of the Island!!!
Taxis are ready when you get off the ship, all taxi drivers are 'official' and you won't have any problem with them. They all do the same tours if you wish, or tailor them to what you want to see. The price will be more or less the same.
One time we shared with another couple in a minibus, which the driver filled with a few couples and two of them are still friends to this day, another time we went on our own in a taxi, the guy was great, gave us a good show around, waited while we went into the caves and took us to where the Monkeys were that he knew and would feed regularly.
Last time we did our own thing, walked to the cable car - went up to the top, had a coffee etc., walked part way back down and got the cable car at the second stop down. Then just looked around town.
The great thing is with doing your own thing, if something doesn't appeal when you get there, you can go onto the next, you are not waiting for others to get back to the vehicle or people going to the toilet etc.
Gibralter is probably one of the safest places you will go to, everyone knows everyone else, it is an island, so not much crime, as there is no where to go!!!
Kate