New York state has seen several boom and bust cycles in its history. At the moment New York City is an economic powerhouse, Buffalo and Rochester are in the midst of a renaissance and the state's wine regions are gaining prominence on the American market. Not everything is rosy, however, and you need only look at the condition of the roads and the dilapidated state of the NYC subway to see that there is political turmoil boiling under the surface.
New York routinely votes Democrat and is a dyed in the wool 'blue state' with several pockets of conservative communities around upstate New York, the wealthier parts of Long Island and some sections of New York City. Despite Democrats typically controlling the governor's mansion and both houses of its state congress, moderate conservatives (usually socially liberal and fiscally conservative) have a sway in state politics. In general you'll find lots of places in New York where conventional party line politics have become blurred. There is also an overwhelming perception that state and local politics tend to be corrupt and easily swayed by the influence of Wall St and monied real estate developers. Many New Yorkers on both sides of the political aisle view the state capital, Albany, in a negative light. They point to the lack of attention paid to public works projects (the state's roads are notably bad and NYC's subway is in a state of disrepair) as evidence of the state's politician's lack of interest in actually governing.
When visiting anywhere in New York it's important to keep in mind that many of the popular tourist destinations did not always look the way they do now. Gentrification, or the process of making a place more refined and appealing, has brought a lot of growth and revitalization to parts of the state, but it has also seen communities driven out of their historic homes and entire neighborhoods and towns rendered unrecognizable to the people who used to live in them. The issue is especially fraught in many Brooklyn neighborhoods, where black communities are being edged out of apartments as developers entice young middle and upper-class white professionals to move in by creating large condo buildings that offer spectacular amenities for a fraction of the rent of Manhattan, gradually raising rents across the neighborhood. The same has happened as city dwellers buy vacation homes in formerly sleepy towns upstate. It's a good idea to keep this in mind when visiting a gentrified neighborhood or town and understand that not everybody is thrilled about the cute coffee shops and $40-a-meal restaurants that have sprung up there.