Applying for jobs long distance

Does anyone have any advice on searching for a job in another state? I'm talking half a day travel by plane. Will hospitals do at least an initial interview over the phone? If a hospital were to call to say they were interested to have me come for an interview, would it be acceptable to say I couldn't make the trip for 3-4 weeks, this would give me time to arrange a couple days off from work and possibly schedule more than one interview in the same trip. I would appreciate any advice on long distance moves and job searches-I'm feeling a bit overwhelmed. Thank you!