In the past months I put together a website for our lab, now called "UCL Cognition and Grammar Lab". Our group has been active since late 2013, but finally decided to build up a stronger presence, especially in light of projects which we expect to involve more public engagement. The lab focuses on language in a range of pathologies (especially stroke and neurodegenerative diseases) and how it relates to other aspects of cognition.
The address is www.cognitionandgrammar.net
I again went with Squarespace since I am quite happy with it and it was easy to show other members how to upload content.