I can assure you that as it is said, New York is the concrete jungle of opportunity. If there is a will you will find your way in this huge city. I have lived in New York City for upward of 23 years and i absolutely love it.
Touching on career opportunities, again New York City is where dreams come true. I would recommend booking a trip to come here and EXPLORE the landscape. Literally you never know who you will see, meet or what career doors can be opened by just visiting a museum, Art Gallery, Coffee Shop, or just a local Eatery. Keep an open mind and you will go further than even you can imagine.
As far as safety, being a native of NYC, i can tell you anywhere is typically safe.
Quality of life is, again, among nothing you would have ever experienced unless your from here. You may be used to big apartments or a spacious house, i can tell you, if your looking to be in Manhattan, Don't keep those expectations. Typical one bedrooms in manhattan are about 600 Sq ft or equivalent to an upscale kitchen. I can assure you we have some of the best pizza on the planet, and that is a personal opinion. Food here is incredible, and the night life is un imaginable. You can literally no to a night club at anytime, bars close at 3-5 am, quant little coffee shops are popping up everywhere so although its a huge city there is still small town feel.
As a Realtor, Federal Fair Housing Laws prohibit me from speaking on Best or worst Neighborhoods. So what i can say is, Chelsea is a very expensive and highly diverse section of Manhattan, with co-op prices soaring into the 10's of millions of dollars. As well SoHo (otherwise regarded as "south of Houston St.) consists of about the same. Expensive Eateries, shopping, and homes make up these sections of lower Manhattan.
For further information about housing refer to Streeteasy,.com
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All the Best,