Assumed: United States jurisdiction, no discrimination component to your experiences.
There is not a legal limit on how much time an employer requires you to be in another city so long as the employer is complying with wage and hour laws, family leave laws, and the like. They may be in violation of their employment contract with you if the contract specified that you were being hired for a position in one city. A four-week trip does not sound like "time travelling" to me, it sounds like a temporary posting in another city.
Similarly, depending on how well the contract is drafted, the state whose law governs the employment, and the company's other behavior you may be able to sue them using material misrepresentation or fraudulent statements about the position you would be taking.
If you want more insight into whether you might have a case, take your contract to an attorney.
In practice, however, the solution is almost certainly not a lawsuit. The solution may be to start looking for a new job, to communicate better with your boss, or to figure out how much money it would take to keep you working doing the job you are actually doing rather than the one you were hired to do, and to negotiate a salary increase. Try posting your question with a few more facts over at workplace.stackexchange.com for more insight into how to deal with the problem professionally.