Where can you play Tabletop Games?

You can play Tabletop Games pretty much anywhere that there's enough table space to play the game.  I suppose the question is probably more likely to be tied to 2 other questions.

Where can I find other people who play Tabletop Games? and Where can I buy Tabletop Games?

Both of these questions can have the same answer when it comes to what's classed as the FLGS.  Friendly Local Game Shop.  Ah but everything's cheaper on the internet even these games why should I buy from a FLGS?  The first question above is why.

FLGS' specialise in selling Tabletop Games, many of these shops also specialise in having events to support Tabletop Games and in turn have developed communities around them to support these events.  It is in these FLGS' and their communities that you will find other people who play Tabletop Games.
In the UK (where I am) you can find out where your nearer FLGS is by visiting the Find Your Game Store website.

In addition to the FLGS environment though there are many many clubs across the world who promote the hobby of Tabletop Games.  These tend to be predominantly War Games related clubs, at least within the UK that is the case anyway.  The Gaming Club Network is a voluntary organisation which helps and supports clubs throughout the UK. Majority of it's member clubs are War Games clubs although you will find that a number of those clubs also support and play other Tabletop Games.

Going back to my original statement about where you can play Tabletop Games, the answer remains anywhere. A lot of people, indeed perhaps the majority, play their Tabletop Games at home with friends.