The Program on Applied Demographics at Cornell University has a great maps page if you're looking for some thematic mapping of the whole state by county. By
visiting their maps page you can select a theme (or metric as they prefer to say) to see mapped out by county for the entire state of New York So for example if you were looking for a feel for what the median age of the population living in each county was, you could select the "metric" on median age and then get the map to show that particular characteristic on a state wide map. It would look like this:
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Mappable metrics include:
Feel free to explore the PAD site. They do some great things with Census data there !