Several people have mentioned Discover Scuba courses without a full explanation. In a discover Scuba course, you are given some basic academic instruction in a classroom, you practice some skills in a pool or pool-like environment, and you have a dive in fairly shallow water.
One thing that was not mentioned is that you can do what is called a referral. In that case, you pick a shop near you and begin your instruction there. You do all the academic learning and the pool instruction locally. When you are done with that, you are 4 open water dives away from certification. You can then get a referral, a document explaining that you have successfully completed that work. Take that document on your vacation and a local dive operator can complete your certification.
If you do use a referral, be aware that the different agencies do it differently. Both SSI and NAUI use what is called a Universal referral system, and you can take a referral from one to a dive shop from the other. PADI uses a different system officially, though. A PADI instructor or shop may elect to use the referral system, but they are neither required nor encouraged to do so by the agency. The difference is that PADI believes that the person who actually sees you performing in the open water should be the one who grants your certification, so in the normal PADI referral system, that is who would be your certifying instructor or agency. In the system used by the other agencies, the instructor/agency that gave you the referral is the certifying instructor/agency.