I am trying to find an older cousin who has vital information that I would like to know in order to do my family history research.
I know the city and state which is Grape Vine, Texas, USA.
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To locate living people in the U.S., I use a combination of the "U.S. Public Records", vol. 1 & 2, databases at Ancestry.com along with a couple of on-line name-and-address databases.
U.S. Public Records generally covers a time-span from the early 1980s (or earlier) to the mid-1990s. Access requires an Ancestry.com subscription. U. S. Public Records usually includes postal addresses during the covered period, sometimes historical phone numbers, and often dates of birth. The data is a little spotty, some people aren't listed at all, sometimes the dates are wrong, and it sometimes confuses people with the same name (especially Sr. and Jr., or in the same town).
The websites PeopleSmart.com (my preference) and PeopleFinders.com will give name and location information (but not address, at least not for free). They both provide some information for free, and more detailed information for a nominal fee. I've only used the fee-based service a few times, as it's rarely necessary.
PeopleSmart lists both current and known past residence locations, which generally go back far enough in time to correlate with Ancestry's U.S. Public Records. The first listed location is usually (but not always) the most recent. The entries also list "related" people, which presumably means those who live or have lived at the same address as the target individual (useful if you can't locate the specific person you're looking for, but maybe can locate one of their siblings or children). PeopleSmart also hooks into the SSDI, and will usually indicate if someone has passed away within the last 10-15 years.
Once you have a current location, WhitePages.com is one of several similar "phone book" sites, that will generally provide a postal address and, if listed, a phone number. A couple of other sites are WhoWhere.com and AnyWho.com (at least one of which gets its data from WhitePages.com).
If WhitePages comes up empty, another source for street addresses are real estate web sites - I've occasionally found an address for someone after doing a Google search, when their name turned up on a list of neighbors of a recently-sold property in their neighborhood.