Since June 15 2017 Roaming charges no longer apply while you use your UK ( pay as you go1 or contract ) mobile phone on Holiday in Menorca. This makes using mobile Internet affordable on holiday but you need to see your providers conditions 2
1you must have an active data plan 2 for example streaming or connection sharing is restricted or not allowed
The main squares in the towns offer free WiFi
WiFi is pronounced 'wiffy' :-)
Vodafone have a strong signal island wide. Mostly a 4G or higher speeds network if you are considering a local SIM card or want to bring a Vodafone base mobile to the island
Internet Cafes will often allow you to plug in your laptop to a wired cable. Prices vary but expect to pay 1-2 Euro for an hour's connection time.
These days it is pretty rare for bars not to offer free WiFi and many have a fibre connection with higher speeds than you will typically have in the uk
Spanish law requires free WiFi to be password protected so if it is advertised you will probably need to get the password (often posted up behind the bar )