postgresql database default location on linux

The "directory where postgresql will keep all databases" (and configuration) is called "data directory" and corresponds to what postgresql calls (a little confusingly) a "database cluster" (not related to distributed computing - it just means a group of databases and related objects managed by a postgresql server).

The location of the data directory depends on the distribution. If you install from source, the default is /usr/local/pgsql/data

In file system terms, a database cluster will be a single directory under which all data will be stored. We call this the data directory or data area. It is completely up to you where you choose to store your data. There is no default, although locations such as /usr/local/pgsql/data or /var/lib/pgsql/data are popular. (ref)

Besides, an instance of a running postgresql server is associated to one cluster; the location of its data directory can be passed to the server daemon ("postmaster" or "postgres") in the -D command line option, or by the PGDATA environment variable (usually in the scope of the running user, typically postgres). You can usually see the running server with something like this:

[root@server1 ~]# ps auxw |  grep postgres | grep -- -D
postgres  1535  0.0  0.1  39768  1584 ?        S    May17   0:23 /usr/local/pgsql/bin/postgres -D /usr/local/pgsql/data

Note that it is possible, though not very frequent, to run two instances of the same postgresql server (same binaries, different processes) that serve different "clusters" (data directories). Of course, each instance would listen on its own TCP/IP port.