I found on the web this project ESP8266 Weather Station by Daniel Eichhorn. It uses an ESP8266 processor and WiFi to download weather from Wunderground and display it on an OELD.
It is wired up like this
This is the result of the example code they provide working
Which was great. But the next day when I switched it on, it did not work. I removed everything, re-installed everything on my MacbBook, no go. I installed everything on a different computer (my iMac), no go. I found it would connect to my router and was given an IP, but would not connect to any site on the internet. I have given up. Maybe my router is somehow blocking it??? Tried to check the router but login admin/password does not work, is the router defunct?