Nabe for empty-nest couple

Hi, we are looking at a move later this year to New York. We are in our early-50s, but try not to act like it. We will be moving from the south, so it is going to be a major culture-shock for us. We are looking for something that will be close to the subway, have plenty of restaurant, shopping close by, and is fairly vibrant. Our budget is going to be between $5k and $6k and it would be nice to end up in a 2br or at least a 1br 1.5 bath. We like the idea of being in a doorman building that has a gym and other amenities. We don't have any pets and our children are all grown, but will be visiting at times. If there is other information that would be helpful, please let me know and I can try to provide it. Thanks in advance for the help.