"Beauty is in the eye of the beholder", as we say.b There are no hard definitions, but here's my take on these words:
Nice - pleasant. Not amazing, but a good feeling without being overwhelming.
Pretty - flowers are pretty! So use that in your thinking: bold and attention-getting but in a bright, light, sunny way.
Beautiful - full of beauty. This is a sincere word, and probably the strongest of all these three words. It also tells me the appeal is inherent, not superficial.