Oct can be rainy and breezy or a heatwave with humid 25C+ temperatures. Have experienced both. Follow weather.com before your trip, the 10-day forecast will give valuable info re: temperatures and rain.
New Yorkers love all black (the city is grimy). An all-black outfit is never wrong there and helps you fit in. New Yorkers tend to dress an bit more formally than the rest of Americans.
I would take along basics: jeans, t-shirts, vests and a pretty top or two, a comfy blazer. When I lived there, I wore hoodies and short showerproof macs a lot and used a backpack to carry my stuff around. I would take a dress (because if it's hot it's really hot - would take along one warm weather dress just in case) and a cardigan (A/C makes indoors cold when it's hot out) and flipflops. Most important, take good shoes. No style experiments, just your most trusted, comfiest shoes. You will walk, walk, walk. If it rains, it rains hard.
If you go to a fancy restaurant, some people will be very chic and dressed up, but in most other places, particular Midtown, anything goes (jeans, jean jackets - and a tourist from Iowa will wear shorts and a neon bum bag and enormous white sneakers). That includes theaters, Carnegie Hall and Lincoln Center.
I think the American uniform for going out is jeans (bootcuts still big there), a pretty/floaty/patterned sleeveless top and cute heels. Wearing this and perhaps a blazer (jersey blazer for comfort?) would make you fit in almost anywhere.
New York has amazing shopping, so bring an empty suitcase with you and check out Target, discounter chains (Century 21, Loehmann's, Marshall's), department stores (Macy's gives all tourists a discount; ask for it), and American chain stores (Club Monaco, Banana Republic, Anthropologie and the cheapo version of GAP: Old Navy). Plus enjoy the variety of drugstores (Duane Reade is everywhere, CVS is even better). SoHo is one big mall, Nolita and Meatpacking district have stylish indie stores, big name fashion is on 5th and Madison Avenues (Midtown and Uptown). Pearl River Market in Chinatown.
If you are into more zany style choices, skip Midtown and hang out in East Village and Williamsburg (Brooklyn; Bedford Avenue and Grand Street).