I assume you also have a fully-charged cell phone and have your essential meds in the first aid kit. Most women I know keep everything (and I do mean everything) in their purse, which means if you get robbed you wind up with nothing. So I would suggest thinking about how you could carry some items separate from your purse, such as:

• The aforementioned or a separate flashlight
• A whistle
• Emergency cash and Debit Card
• Copy of ID
• Emergency contacts

Maybe you've considered these and dismissed them, but some other items to think about:

• Small mace/pepper spray (if legal)
• Swiss Army Executive knife (usually permitted where a larger knife won't)
• A card with some needles, thread and safety pins.
• A feminine napkin (can also be used as an improvised trauma pad).
• An energy bar, granola bar, Clif bar or similar.
• Chewing gum, breath mints or hard candy.
• Emergency poncho (the kind that folds-up real small take up almost no room)
• Flat-folding N95 mask
• Wet-Naps (good for more than washing your hands)
• Small notepad and pen/pencil
• Spare contacts/glasses

I'd also carry a small subway/street map because I'm not that familiar with most of the city.

I'm thinking scenarios like being stuck on an elevator or in the subway, or hit by an unexpectedly severe storm.