I want to install a new 30 amp receptical, what size wire would be needed to run about 20 ft from the 30 amp breaker. Will it then be safe to plug a 20 amp plug from my travel trailer into it with a dog bone type connector, which will run a microwave a TV and a roof top air conditioner. I would not need to run both the micro and air at the same time, but could I?

#10 copper wire is rated for 30 amps. You can use cable to match what is in your home.

Using a 30 amp circuit for a 20 amp load is fine.

It specifically answered the question!!