I am being sued in another state. Is there anyway to have the case dropped without going there?

It is not clear if the action against you is in New York. Your first enemy is time. You must act very quickly to prevent a default. The options are (a) do nothing, (b) fight, or (c) settle. If you fail to file papers within the time permitted, you can be defaulted, and a judgment could be entered against you. If you are not already defaulted, you should act very quickly to avoid one unless you decide to do nothing.

Doing nothing is dangerous because judgments bear interest, and can open roads to harass you through discovery, liens and credit reports. You say the suit is for $1,600, but you should read the complaint very carefully to see if they seek attorney's fees or other damages that could inflate the amount at stake.

Settlement may be possible, but they won’t likely settle when they can just default you. You should answer or move to dismiss first to eliminate that leverage. If that is your choice, and you decide not to use an attorney, you could call the court and ask for their office-for-the-self-represented, who should be able to tell you how to answer the complaint.

If you decide to fight, you can hire a lawyer where the suit is, who is armed to fight these battles. A lawyer will determine if there are good grounds for a pre-answer motions to dismiss, and can take the fight from there. If you try to fight it without a lawyer (generally not recommended), you will, sooner or later, be required to go to court, at least once, and maybe many times, or you could be defaulted for failing to appear in court.