Agree with all of the above. For NY you'll want a warm, weatherproof coat and boots. For LV, you'll want to be prepared for likely wind and possible rain, but temps will probably feel more like fall than winter. When the sun is out, it warms up pretty significantly, and once the sun sets the temp can drop down to freezing, so layering is key. I'd bring a mix of dressy and casual. Like Laura says, anything goes. You'll see everything from cocktail dresses to Hawaiian shirts, stilettos to flip-flops, all in one place. (OT: If you decide you want a break from the Strip, I highly recommend renting a car and going out to Red Rocks for a day -- beautiful desert landscape, mix of car-accessible vistas and short hiking trails.)
Honestly, NYC has a huge range of dress, too, and it varies so much depending on where you're staying and what you'll be seeing. Bright colours generally scream "tourist" -- it is a city devoted to black and dark neutrals -- but there are folks like Angie who do polished brights with panache and make it look completely natural. And yes -- make sure your footwear is comfortable, well-broken in, and walkable! You'll put serious miles in in both cities.
