The reason why she did that is because (little-known fact here, even among Catholics) a parish is actually a geographic division, so whatever parish you (or, in this case, FI) live(s) in is the place you should start.
There are two ways of being a “member” of a parish: find one you like, start attending Mass there regularly and formally register as a member (i.e. sign up, what most couples do if they need to establish membership in a parish to have their wedding there), –or– figure out what parish’s territory you live in. Not many people know this, but a Catholic is “automatically” a member of the parish wherever they live, and they have a right to receive their sacraments there. (You may not be delighted with the parish, the priest, etc., but that’s another matter – you at least have a parish that has to recognize you/FI as a member for the purposes of getting the ball rolling on your marriage prep.)
You may need to do some juggling when you move, of course – Fiance will probably need to find a parish in your new city, and there’s a little extra bureaucratic complexity whenever Catholics get married in a parish other than their own. Also, if you are unbaptized, there is some extra paperwork you’ll have to do with the diocese (and you’ll need to check on whether that’s the diocese in NY or the new one where you’re moving). That won’t be too big a deal, though.
One final thing it would be good for you to know right off the bat, too: most of the time Catholics have the option of having a full wedding with Mass (meaning a wedding that includes Communion, takes about an hour or a little more), or a wedding without Mass (so, no Communion, and it will last around 45 min.) When a Catholic marries an unbaptized person, it’s automatically going to be a wedding without Mass. Your Fiance might need to break that news to some of his relatives, etc., so it’d just be good to make sure he knows.
Also, since he’s the Catholic half of the couple, things might go a little more smoothly if he is the one to make the calls, talk to the parish secretaries, etc. He will need to make arrangements to get a copy of his Baptismal certificate, etc., at some point, and I’m sure he is much more likely than you are to know the details of where and when he got baptized, confirmed, etc.