Whew! August will be the 3 H's - hazy, hot, and humid and it will likely rain/thunderstorm at some point while you're there. Many residents leave the city on the weekends so it will likely be a little *less* crowded than normal but if you don't know "normal" you'll stilll likely find it crowded...if all of that made sense! LOL
Personally, I would avoid shopping in Times Square (I think most of the stores there are either chains you can find in any suburban mall in the US or cheesy tourist shops). Since you've never been to NYC, you'll likely want to join the tourist crawl down 5th Avenue and browse through Saks 5th Avenue, the Tiffany flagship, etc.
Macy's Herald Square on 34th Street is an absolute ZOO, as is the Manhattan Mall nearby.
When I visit, I head downtown - to SoHo, Tribeca, Chelsea, the Village for designer and indie boutiques. Century 21 is a fun store to roll up your sleeves and dig for designer bargains.
I also recommend
Barneys flagship on Madison Ave. at 60th and Barney's CO-OP in Chelsea.
Outside NYC, you can take a bus about an hour or so to reach Woodbury Commons, a premium outlet center with stores such as Burberry, YSL, Bottega, Chloe, Gucci, Tory Burch, etc. You can google it for location and transportation information.
You can get 1/2 price tickets for same-day Broadway shows at TKTS booths - one near the Marriott Marquis hotel near Times Square and the other in South Street Seaport.
You can walk through Central Park and across the Brooklyn Bridge - great views of the Manhattan skyline.
For packing, wear hot weather clothes and bring a wrap or cardy for A/C inside. New Yorkers dress up a bit more for drinks/dinner/clubs so bring some nice "going-out" clothes.
Have fun!