When you are traveling outside of the United States chances are you will be spending money on things like souvenirs, food, transportation, and entertainment. Even if you are staying at an all inclusive resort or on a cruise, where most things are included, you are likely to need some cash. The question is will U.S. dollars be good or do you need to exchange for the local currency? My personal experience in the Caribbean and Mexico is that the U.S. dollar is accepted most everywhere. Keep in mind they may give you local currency as change so it always helps to check the exchange rate. Many places will have a posted exchange rate so it is always good to look for that or ask before completing a transaction. Large expenditures may not be legal in Mexico and may have to go on a credit card or be in local currency. On resort you can generally charge most things (tours, spa, gift shop) to your room if you gave them credit card information at check in.
If you are going further from the United States and vising Europe or other Continents it is always good to take a little starter cash in the local currency. This can generally be done at a local bank. Not all banks do this. Most will charge a fee and will likely take up to 2 weeks to get the funds you are requesting. My local bank charged me $5 and will take 2 weeks to get me Euros, Jordanian Dinars, and Emirati Dirham for my up coming cruise. I could use ATM's in each area or exchange at the airports to get local currency but it is nice to have some to start out with and I avoid ATM fees that can really add up as well as international fees. I also have less concerns about having my card skimmed. The bulk of my costs will be prepaid or put on my ship account and settled with the card I gave them while setting up my account with the cruise line. The goal is to spend as little precious time during vacation exchanging cash or standing in line at ATM's. I would not advise you carry excessive amounts. You always want to use safe travel basics. What you do carry should be in a zippered or difficult to get to area on your person and should never be flashed in public. Always keep this and all valuables in the safe at your hotel or on your cruise.
What do you do with any leftover local currency? Many keep it as souvenirs of their trip. In most places there are opportunities to donate the funds to help out local charities. You may choose to leave it as a tip for your maid or room steward. If you have a large sum you may return home with it and do a reverse exchange similar to how you got the currency in the first place.
I hope this help make your trip more enjoyable. As always travel and explore but be safe and mindful.