It's hard to bring the wrong lens to Manhattan. But you will need to pick your subjects to match your lens. I actually did just fine with a K-r and its 18-55 kit lens a few years ago near Christmas. With dim light, I let the ISO scoot way up there. The noise gave my images a certain grittiness that was well suited to the city. Unless you want spectacular photos of the Statue of Liberty from Battery Park, I would take the 15 and the 18-135 ... and use the 18-135 most of the time. 135 really isn't long enough for the Lady, so you will probably need to crop.
While a tripod might be useful, hauling one around can be a pain. Have you considered a monopod with a quick release?
Buy one
without the metal spike. And enter museums using the monopod just like you would a cane, with the camera stored. Tripods are an almost universally banished device in museums. Canes or similar sized walking sticks used in place of a cane (so long as it does not have a metal spike) are often admitted - and so long as you are bold and using it as a walking assistance device. If it is fully collapsed or fully extended when you enter the door, you are out of luck, it is now a piece of photographic gear and you will typically be forced to check it. If asked (rarely happens to me), you didn't want to carry both a cane and a camera support. At worst, staff check for that nasty spike foot. If it is a full rubber boot (and not one of those boot & spike combinations) few museum staff will question your need for a cane. I have toured museums in Europe and North America. In some, I had to check my camera - but never my monopod.