It depends on what you are going to do. If you explore on your own, I have yet to find a taxi, bus, tram or train that takes travellers cheques in USD.
The tiny shops almost never take them.
Also, if you do find a store that will take them, the exchange rate won't be very good. Might as well use your AMEX card.
I always bring local currency. The amount depends on what we are doing.
SS Norway (12 times) '85 - '97; Radiance OS 06/01; Island Princess 11/04, Grand Princess 11/04/05, Golden Princess 7/21/06, Golden Princess 2/24/07, Explorer of the Seas 12/23/07, Island Princess 11/15/08