Divorce laws are different in every state. There may be advantages to filing in Florida vs. New York. Florida is a no fault state and your choice of state, "forum" may affect the property division, if any. Second, are there any children of the marriage? If so, Florida law says that jurisdiction is proper where the parties last resided as Husband and Wife and the home state of the children will be extremely important in working out any timesharing issues with your children.
If there is no property/marital debts/marital liabilities, and no children then a divorce in New York will be fairly simple, you may have to personally serve her here in Florida or you can also serve her by publication, if such a form of service is allowed in New York. IF there are no issues to be decided and your objective is to simply get a divorce, then she may just sign a waiver stating that she accepts service of the divorce and that she doesn't intend to contest the action.
Either one of you can file in your home state assuming you meet your home state's residency requirements. There may be advantages to filing in Florida as opposed to NY. You need an attorney's help on this one.
Right out of the box, your question raises the issue of jurisdiction and choice of law. For example, where can or should you file for divorce? The choice of state can have very different consequences, because of the different state laws, on issues of property division, grounds for divorce, and child support, to name a few. For example, Florida offers you the ability to obtain a "no-fault" divorce, while New York would require fault. This significant difference in law may be crucial in you decision whether to file for divorce in New York or in Florida. I would recommend you conduct a preliminary search on the internet to compare the laws in New York and Florida on the issues that are of utmost interest to you, then take the preliminary information you find and consult one or more attorneys to discuss the facts of your specific case, and to address your particular issues and how they might be handled differently in the different states. Once you have determined where the laws would be most favorable to you, you can make an informed decision as to how (and where) you should proceed. Good luck.
Sign up to receive a 10-part series of useful information and legal advice about the divorce process.