Unfortunately, the Google Fiber network in Raleigh and especially Durham is not that extensive. After a brief period of development and growth, only a limited portion of the Triangle area is served by Google Fiber with further rapid development and laying of fiber-optic cable having been put off. Other metro areas like Austin and Salt Lake City have much more extensive Google Fiber networks. That being said there are other options such as Brightspeed fiber, AT&T fiber, and Ting fiber available. Everyday more fiber cable is laid in the Triangle.
In Durham, high density areas close to downtowns have Google Fiber service, while only some outlying more suburban areas do. For some reason google has not put in much Google Fiber in at all in Durham, which is strange since other areas like Chapel Hill and Cary are filling in rapidly.

Google Fiber Raleigh and for the greater Triangle has a home base at the Google Fiber Space in Glenwood South near to Downtown Raleigh. At this Fiber Space location you can learn more about the Google Fiber offering and your potential eligibility for the service.
With extensive costs including new fiber optic lines, utility poles, digging, and approvals from city leaders - executing this type of project can be incredibly intensive. Fortunately however, many residents of the Triangle area are able to enjoy Google Fiber and are also able to have access to other gigabit speed internet service providers.
Here's the map for the more extensively laid out areas, such as Raleigh, Cary, and Morrisville:

Typically Google Fiber is 10-100 times faster than existing broadband, access to this kind of fast internet can increase a neighborhood's property values as more people (especially those working remotely) start to look for homes with fiber. To learn more about Google Fiber in the Triangle area and see if you can get it in your home, start by putting your address in Google's Triangle fiber page.
Some example neighborhoods expected to have fiber due to their locations or large size are below:
-North Hills (already has Google Fiber for the most part)
-Anderson Heights
-Belvidere Park
-Boylan Heights
-Cameron Park
-Five Points
-Glenwood-Brooklyn
-Hayes Barton
-Oakwood
-Mordecai
-North Hills
-Ridge Road
-The Village District (has Google Fiber already in some areas)
-Woodcrest
-Forest Hills
-Hope Valley Farms
-Lakeshore (already has Google Fiber)
-Old North Durham
-Trinity Heights
-Trinity Park
-Watts-Hillandale
-Woodcroft (a lot of Woodcroft already has Google Fiber)
-Estes Hills (already has Google Fiber for the most part)
-Coker Hills (already has Google Fiber)
-Historic District
-Ironwoods (already has Google Fiber)
-Lake Hogan Farms
-Lake Forest (already has some Google Fiber)
-Meadowmont (already has Google Fiber)
-Parkside
-Southern Village
-Winmore