The second one is definitely correct. The 'of' is actually part of 'enough of' and not 'of being'. When you state on it's own 'I have had enough.' it is a complete statement. It does not include a subject, so the listener must guess. Maybe you are eating, they will assume you have had enough food. Maybe you are sad, and they will assume you have had enough bad experiences. If you are talking about quantities, you can omit the of - "I have had enough soup" But when you talk about an activity like being nice, or being sad, or going to school, it not just a quantity of things. It is an ongoing activity. In this case, we use 'of'. To me, it means 'I have reached my limit for how many times I will engage in this activity' There is probably a gramatical rule for this. but I don't know how to describe it technically, sorry!

The difference is -- the first ones are incorrect. :) "I've had enough of being nice" and "I've had enough of being there" are correct. You should always say the "of".