I would say the most appropriate way to act is to act how you want to be treated. I wouldn't worry about acting like a local, because you aren't a local. People will know you are a visitor from a mile away (and then approach you trying to sell you something). Respect generates respect, for the most part.
I would suggest that on an average interaction, a friendly greeting and departure are common. If someone is selling and you aren't buying, like halfwaytree said, a firm but respectful "not interested" is most appropriate because its the truth. Or say whatever the truth is in regards to your level of interest when someone has something to sell you.
A fist bump is a friendly greeting, but I only do that to people I see and talk with regularly. I hug friends I have gotten to know over the last few years.
If you happen to have a disagreement or conflict with someone, try to handle it with as much grace as you can muster. You are a visitor and guest in someone's hometown, neighborhood, restaurant, or hotel.
Be as genuine as you can. Do not be deceitful. If someone asks you a question that you don't want to answer, say "no thanks" rather than lie.
Men, and possibly women, may advance upon your girlfriend. Again, with as much grace as can be manage, a firm but respectful, "not interested" is important in this situation.
The only ones who can tell where that "line" is and when it is crossed are you and your girlfriend... an ANY situation. If you are uncomfortable, walk away. You may be insulted as you leave, but words are only words. For the most part, people on the beach are looking for one key outcome: that you buy something from them, and sometimes for them. Know your own limits and boundaries and stick to them.
