Хорошего пути and наслаждайся своим временем в Москве are quite good actually, it's just the first one doesn't really fit in and the second is something uncommon to say.

Хорошего пути is about having a nice time getting to a place and not about having a nice time at the place. There is a common phrase though "счастливого пути", yet again it means just the same thing as хорошего пути

Хорошо (тебе) провести время в Москве - Basically - have a good time in Moscow, literally - good spending of time in Moscow to you.