The term used to connect a number of computers within the same location or in close proximity is

Connecting computers in one place or close together is done by a Local Area Network.

A WAN spans wide geographic distances, such as between cities or countries, not a single location.

A PAN is a personal-area network around one person's devices, much smaller in scope than a room of computers.

Only the local network fits the described short range, so a combined answer does not hold.

A LAN typically uses Ethernet cabling or Wi-Fi within the premises.

LANs are common in offices, schools and homes.