Is it best to get a taxi or the shuttle bus from the airport
It depends on where you are trying to get to. If it is the Old Town or in Gruz I wouldn't waste my money on a taxi.
Shuttle is 40 HRK one direction and taxi 250 and more.
Yes, where is your accomodation, in which part of the town?
Yes, plenty of taxis waiting outside the arrivals building. You could also ask the airport shuttle to stop at Mlini.
It’s the old town. I think it’s not far from where the shuttle bus drops off. Our grand daughter and boyfriend only have 2 and a half days in Dubrovnik so didn’t want them to have to hange around too long waiting for a shuttle if they’re not very regular.
The shuttle buses are timed to meet each flight. When I've used them, yes there is some waiting, but not much and the journey time is the same as a taxi.