Lawsuits to address immigration delays and denials are filed in Federal District Court. That is because immigration law is all federal. As to which district court, this is guided by 28 USC Section 1391.
According to the law:
A civil action in which a defendant is an officer or employee of the United States or any agency thereof acting in his official capacity or under color of legal authority, or an agency of the United States, or the United States, may, except as otherwise provided by law, be brought in any judicial district in which (A) a defendant in the action resides, (B) a substantial part of the events or omissions giving rise to the claim occurred, or a substantial part of property that is the subject of the action is situated, or (C) the plaintiff resides if no real property is involved in the action.
This gives immigrants and their sponsors some options as to where to file. The most common places immigrants file these cases is where (in the US) they or their sponsor live, Washington, DC (since that is where the federal government is principally located), or the location of the service center processing their immigration matter.
There are instances where any of these could be the best option. All things beings equal, where you or your sponsor live is typically the best option. The reason for this is because this is the option where the Government is least likely to successfully seek to transfer your case elsewhere. Transfers are not the end of the world, but they can be costly, add further delay and can result in having your case heard in a less friendly court. That said, if the case law is bad where you or your sponsor live or the local US Attorney’s office is hostile to immigration cases, then other options make more sense.
Where to file can be a crucial decision that has a major impact on the success or failure of your case. Ultimately, this important decision should be made in conjunction with the advice of an experienced federal litigator.