no do not use a microwave ..they are dangerous ..they change the molecular structure of the food, creating chemicals previously unknown to the planet.
Instead buy an electric cooking pot ..in addition to the tea, you can cook soups, stews, even eggs and stuff in it. Then if the hotel or campground (get one with electric hookups) does not have a refrigerator, get lots of their free ice and put it in a small cooler to cool it down. This should be fine..if you are super worried, use dry ice for the cooler..with these two things you can make your tea and go anywhere but please do not use a microwave for ti or anything..they are not good at all.
EDIT--sorry I did not see northstar's suggestion on the microwave but still I would go with the cooking pot as microwaves also change the molecular structure of water and are never safe to use. Tom who posts here has a big paper on how bad they are.