For local moving, get some rubbermaid cans and containers. Put the fish in one, corals in another. Put rock and sand in cans. Use the water out of your tank to cover rock and sand. Set the tank back up and run with skimmer for few hrs, using as much old tank water as possible. Keep a heater and powerheads on the fish and corals. It basically the same to move it from room to room or city to city unless the trip is more than several hours.
move the tank morning so you have plenty of time to set up. It will take longer than you thought.