You can try various sources for this kind of information.
1. Many towns have excellent websites that have already gathered Census data for their town. You can find each towns' official websites through Google. For example, you can Google Town of Brookhaven official website. On each official town page, use the search function or other navigation tools to find census data. A good search term would be census.
2. State and County QuickFacts: This US Census Bureau page "contains statistics for all states and counties, and for cities and towns with more than 5,000 people." Pick NY state from the drop down list, click GO and you will have a list of statistics. Right under the tabs near the top, make sure to Select Suffolk County and then click GO.
3. American FactFinder: On the home page, type the name of the place you are looking for into the Community Facts search box. Once you search, you will get popular information for the place you want, including figures on race from the American Community Survey.