Okay here's the updated list so far:
1. Per the late great Walter Greenspan, use the U.S. Census Bureau's Address Search function (scroll down a bit and look on the right half of the page to find it) to find out exactly what town, hamlet, school district the home is in.
2. Find accurate tax numbers (mynassauproperty.com is a great resource)
3. Is the house in a flood zone? Find a FEMA map, or go to floodsmart.gov. If you're even remotely concerned, call a local agent and get a rough quote for flood & homeowners insurance.
4. Read as much as you can about crime, income, demographics on city-data and elsewhere. Search the area name on Newsday, Google News, etc. See if there's a NYT "If You're Thinking of Living In..." on your new town. Search on YouTube (I watched someone jet ski down the street past a home I had put in an offer on during hurricane Irene), search on Facebook (who lives in this town? what do they say about it? are there groups created to address problems in the neighborhood?)
5. Call the school district you think you're in and confirm the schools you're zoned for. Read reviews of those schools (bearing in mind the tiny sample size) on GreatSchools.org.
6. After you've exhausted all the information on City-Data, use a tool like PropertyShark to get a ton of specific information about the home and neighborhood - owners, previous sales, square footage, additions/ improvements the government *knows* about, comps - the site is subscription-based but you can get a few free trial searches.
7. Walk the area, day & night. Chat with the neighbors. Use Google Maps.
8. Without panicking, look for potential environmental hazards (e.g. the Bethpage plume, incinerators, huge power lines etc) and localized health concerns (e.g. cancer clusters).
9. Time your commute.
10. Find out if there are flight patterns directly over your house. I used
flightradar24.com to literally watch planes going around in the sky near my house.
11. Sex offender lookup:
National Sex Offender Registry - Family Watchdog
12. These should be handled by your real estate "team," but you'll need a home inspection, a new survey of the property, and you should check to make sure there are no open permits on file.
13. Find out if neighboring homes are occupied by owners or tenants who come and go without the same kind of investment in the neighborhood an owner would have.