Tea houses and tea rooms, even tea gardens, have existed all around the world where people drink tea. Because drinking tea is a perfect way to socialize, to enjoy spending time with people you know, or those you don't know yet. Tea houses provide the perfect environment to relax and enjoy the company of your friends, family, business associates, or whoever.
While in one sense tea houses are the same the world over, because they involve drinking tea, they also reflect the differences in culture of each part of the world. So, Japanese tea houses were designed for the very formal Japanese tea ceremony while British tea houses, or more commonly tea rooms, were established to allow respectable women to socialize in public without male company. Tea houses are also a great alternative to the pub or bar where alcohol is served, and thus are very popular in Muslim countries such as Turkey, and flourished during times when temperance movements were strong and during Prohibition in the United States.
So tea houses tend to be family-friendly, although some of the "stuffier" British establishments really cater only to women, or at least adults, and would prefer no children running around making noise, and certainly the Japanese tea house is no place for a child!
Image of Tea house from Wikimedia Commons