Can you visit other states without using immigration flights?

Only during weekend events, Valiant Conquest or Wasteland King, where you can attack or gather.

If you have enough immigration flights, you can choose to enter the state without immigrating to it and check out the state or even locate a member of a alliance you knew and are friends with to mail him or her. I have a friend I have known the longest in the game when we were in the same alliance in the state we were in together and we visit every now and then.