1. Have a nice trip - Хорошей (or any other adjective that have a sense of good/bad) тебе поездки (or any other noun similar in meaning to поездка).
Few things:
You can use any other adjective instead of хорошей, provided the new adjective has a meaning of quality like плохой, ужасный, великолепный and so on.
The word тебе is not mandatory, you may just as well skip it.
You can use any other word instead of поездка if the new word is similar in meaning to поездка

2. Enjoy your time in Moscow. - Хорошо (тебе) провести время в Москве. Other variation of that are possible of course.