Thanks for all your answers!

"I have a gift for you" is about the intention. It means you have a gift with the person in mind. If someone said to me, "I have a gift for you," I would smile and say, "Thank you! What is the gift for?" "I am giving a gift to you" is about the act of handing a gift to someone, either now or in the future. If someone said to me, "I am giving a gift to you," I would assume they are about to hand something to me. Either way, the person will thank you for a gift. But "I have a gift for you!" is a gentler way of saying it.

Easy way to remember this: I gave a gift to Paul I bought a gift for Paul These sentences basically mean the same thing. Only difference is that: The first sentence is just discribing the interaction between myself and Paul. Through context it might be implied that it was his birthday and I had bought him the present...but the actual sentence doesn't give any indication as to where I had got this present and why I was giving it to Paul. The second sentence is discribing something that I did and the reason why I did it. Doing something FOR someone is implying that the person wanted that something and you are helping them get it.

For you has a more positive connotation (you did it to help that person/thinking about them): I have a gift for you!/ I worked hard for you. To you can either have a negative connotation (you did it because you didn't like that person), or is more about movement towards that person more so than helping them: I did something bad to you.../ I brought these shoes to you / I came to you for help.