Just something to remember get the license in the state you plan to marry in. For example, if you live in VA do not get a marriage license in VA, thinking you will save a few minutes or the register of deeds will have it on file when you return. Just get the license in NY and make sure you get a copy, if you ever have to answer questions like for a security clearance or something state you were married in *blank* county in NY.
In NC our marriage license has it printed on it something to the extent "can only be excuted in the state of NC" something like that. Only means if a couple gets a marriage license from a county here, they have to get married somewhere in NC, not in VA, TN, etc. If you were married in NY and moved to NC, the marriage in NY would be honored in NC; however I have no idea about a gay marriage.
If you know the county you plan to marry in check their clerk of courts, register of deeds, or maybe vital statistics web page, probably has all the information you need; what type of ID, how much does it cost, do you need a physical, etc. Even if a minister conducts the ceremony one of those offices will record the license. They could also answer your questions if you have concerns if another state would recognize their marriage license.
I do weddings pretty regularly at the court house, people call all the time with similar type questions.
Edit: Just remembered we issued criminal papers for bigamy not too long ago. Lady married a guy here in NC recently. Come to find out she was actually still married to a guy in Texas or somewhere. New husband called the cops to see what could be done since he did not know she was still legally married. Cops called Texas and confirmed she was still legally married in Texas and charged her with bigamy here.