I don't want to go out with my date after promising to go
Why did you change your mind to go out with your date?
I'm tired. I don't want to go out.
I know we all get tired, but you still made a promise. Promises are always meant to be upheld and if you just told him you're tired then he may be considerate and do something more relaxing with you. Good things can come out of honesty, instead of being negative and ghosting him.
I'll admit that I broke the promise and I'll apologize, but I did it because I'm tired.
I believe you handled the situation appropriately. We all get tired and I am sure they will understand that you don't want to go out, perhaps at a later time then.