Here we have a classic example of difference between British and American English! As a speaker of the former, I would certainly use 'laze around'' -or I am having a lazy day. I would NEVER say chilling out, but that maybe more due to my age than anything else! Having a relaxing day; having an at-home day - all of these convey the same meaning. 'chilling' and 'hanging' are not only American, but probably more common with the younger generation, so when deciding which to use, assess your audience. If it is a bunch of grey haired old English ladies, say 'lazing around'. if it is a bunch of 20-something Americans, go with chilling/hanging!

Chilling out is the most popular informal term you can use. I never heard somebody use lazing around to be honest. Another one that is like chilling out is "hanging out/around"