I live in Queens, but I have a few suggestions:
For sightseeing, flattering jeans with a flattering top are just fine. Instead of sneakers for walking, wear flats with sneaker bottoms (I got mine at Payless- comfy, cute, in great shape, and cheap). Do carry a pocketbook (please, please, please do NOT use a fanny-pack. It smacks of tourist and just looks bad), but make sure that it’s not too flashy. In general, keep it simple.
For nights out, you can wear dark, flattering jeans with a slightly fancier top, or you can wear a flattering skirt with said top. Wear low heeled pumps or slingbacks and carry a smaller purse.
Those are my suggestions. I hope this helps.