Would you like to have dinner with us? Will you have/Won't you have dinner with us? (Do) come and see us tomorrow (informal) What about coming/How about coming to our house? (informal) Do you feel like coming/Do you want to come to a party? (informal)
Well, that's very kind of you, but I won't be here tomorrow. I'd love to, but I'm afraid I have some work to do. Well, thank you very much, but I'm afraid I can't. I'm afraid I won't be here, but thank you all the same.