After one year do you have to switch cities?

If you do not take a break and go back to your tax home (and, by the way it doesn't have to be a 30 day break) all that will happen is that you are now consdered a Florida resident and must pay taxes on your housing stipend. You also would have to pay taxes on any per diem amounts that mey be included in your pay.

Now, if you do not have a tax home a reasonable distance away from where you are now (far enough not be be able to drive to after work and get a decent night sleep-according to IRD standards) you should already be paying taxes on your stipend and per diem, so might as well stay.

Your recruiter is incorrect in that you must leave for 30 days. All you have to do is visit your original tax home on a periodic basis and must have substantial ties to the area. It helps substatiate things if you go there to have medical issues taken care of at the tax home location, a drivers license, an place in the residence that is not shared [like your own bedroom with your things in it], pay rent, etc. Also, if you have that, all you have to do is go there for a visit after the contract is up, work a couple of shifts agency & return to a new lease and new contract in Florida maybe a couple of weeks later.

You must make things temporary to say that you are not a permanent worker [by IRS definition] and no matter what, returning to the same place and winding up working there for over a year, is going to make it hard to not have you considered a permanent employee (only resulting in you having to file taxes as a Florida resident and having your stipend taxed)-that is, unless you can show ties to your pother residence and break up work in between assignments [most do that through agency work already lined up before they come back for the brief visit].

Another thing you might consider is that the travel company is the one that issues you your pay and the IRS normally doesn't know where you are actually working as your w-2 comes from the company. You can always sign up with another company and have them continue on with your contract, since your company doesn't want to re-sign you (makes you eligible to have another company represent you no matter what your contract may say-you do not have to tell your company where you are going, unless they hold an exclusive contract for the hospital and would find out about it because of that).

It might have nothing to do with taxes. It might a hospital policy about the use of travelers that is part of the agency's contract.

Many hospitals refuse to hire a traveler on a "permanent" basis because that would encourage all of its regular staff to quit their jobs and go work for the agency instead of the hospital. That would be too expensive for the hospital if many of its nurses did that. In other words, "Why work for the hospital if you can work for the agency and be paid more for the same work?" To prevent that from hapening, the hospital insists on any travelers being "temporary" employees only and places limits on how the nurse can work at that hospital.

For example, my hospital will only allow a traveler to stay here for 2 consecutive 13-week contracts. Then the traveler must either accept a regular job here or leave for at least 13 weeks before we will allow them to return.

You are absolutely right. I forgot about that aspect of it because of the way the OP worded the question- saying returning to the city instead of the particular hospital. It sounds to me like the company is setting the rules, rather than the hospital; but, who knows?