Pee is an informal but common word that means "to urinate." Of all the slang words for bodily functions, this is one of the least offensive.
Though it's not very naughty to talk about peeing or taking a pee, this term is a little childish. However, saying "I have to take a peepee!" or "My dog is going number one" are even more childish. No one will blink when you say you have to pee, but they're probably not thrilled to get this information either. Unless something in particular about peeing needs to be discussed, it's best to just say, "I have to go to the bathroom."