Generally, it will be the state you spend more time in, at least for tax purposes.
There is a concept called "domicile". Your domicile is where you are considered to live permanently, and you only have one domicile. Factors that can be used to determine where your domicile is include: sources of income, significant professional relationships (your doctor, attorney), and significant social relationships (friends, church, clubs, etc.)
Where you will run into tax problems is when your domicile conflicts with state law. For example, you might argue that your domicile is in Florida, based on the factors mentioned. But if you live in New York more than 183 days of the year, New York will consider you a resident and require a resident tax return. Every state has different laws on residency for tax purposes, and you don't mention the states you are talking about.
You will need to visit the tax web sites of the states involved and review their rules on being a resident or non-resident. The easiest thing to do is to then arrange your dates so that your domicile matches state law (such as, if you really want to be considered a Florida resident, stay in New York less than 183 days.)
You may want to consult a professional tax advisor. Convincing a state that you are domiciled elsewhere and don't owe them tax, even though you spend a significant amount of time in-state, can be tricky and result in audits and other problems.
