Hello Aga
Welcome to the myTobago forum.
I am not superstitious, but I hate answering questions like yours. Please also understand that my reply ONLY relates to Tobago, not Trinidad, where frankly I would be hesitant to even walk outside a hotel on my own. I exaggerate, of course, but only to stress the point.
Your question is difficult to answer fully, because of the risk of causing offence. So, please understand that I am simply being frank and honest. Yes, you are likely to encounter some degree of attention, on the beach and elsewhere. Tobago has always been a very popular destination for single ladies, many of whom come to Tobago hoping to commune with the local community, shall we say. I'm not suggesting for a minute that this applies in your case, but it is important that you understand this situation as it will help you to understand the amount and nature of the attention you receive. Most of these young (and not so young) men can make charming and amusing companions. However, the local culture is extremely macho and it is critical that you bow to that whilst in their country and under no circumstances show them disrespect, particularly in front of other locals. In short: you will be perfectly safe on any of the popular beaches, but always sit with sight of other beach users, local or overseas. As anywhere in the world, leaving the beach area with someone you don't know is highly risky.
Other than that, my personal feeling is that you are should have no trouble driving around the island and going wherever you like. However, you will find such trips very much more rewarding in the company of a guide, if for no other reason than the fact that a decent guide will be able to point out features and sights that you would otherwise miss. Quite frankly, one stretch of rainforest or beach is much the same as another, but the entire situation can be transformed with a knowledgeable guide to tell you the historical background.
I hope the above helps.
