Weather in late May early June could be anywhere from temperate to soaring heat.
Will you walk a lot in the city? Are you used to walking a lot? I am a constant walker but I walk even more on big urban vacations and my suggestion is to ignore the advice about limiting footwear. A change is BETTER than a rest when you are in NYC. Options and switching footwear out improves your comfort as well as your fashion quotient. If I am going for 5 days, I always bring at least 3 pairs of shoes! For several weeks, I'd bring four (at least). My priorities would be:
One all day walking shoe that looks great with various outfits. (Or bootie).
One rain proof or at least rain worthy shoe or bootie that is comfortable for all day walking. (Could be thunderstorms at that time of year.)
One "dressy" shoe, sandal, or bootie (depending on time of year) for going out in the evening. In May/ June, this might be what would count as a heeled shoe for you.
Angie always says to build your outfits from the footwear up. It's great advice. But also for your trip -- consider what you will be doing and then pack accordingly. Do you have a shoe that works with each proposed outfit? If not, either change your outfits or add a shoe.
I am super conscious of weather issues. At a transitional season like the one you are facing I would be checking weather reports for the weeks before the trip and re-calculation my packing based on that. You might need two rain worthy shoes, or two pairs of sandals. Depending on temperatures and your heat/ cold tolerance.
My favourite footwear in past visits to NYC (depending on season) -- low wedge gladiator sandals; low heeled booties. I would not walk around on shoes without any cushioning or support. I do not care for walking in shoes that have a flat rigid footbed and Cons without insole or wedge heel are a nightmare for my particular feet. (I do have some Hi-Ness Cons that I find comfortable but they are a low wedge.)
