What is the difference between putting 今天 before or after the subject? 我今天去电影院
今天我去电影院

I've also noticed that other words can be before or after the subject:

如果我是你
我如果是你

What is the difference in nuance of placing such words before or after the subject, if any?
It's really a matter of emphasis. The greater emphasis is on the word that goes first.

今天我去..., means, Today, I am going out...

On the other hand, with 我今天去...,

the emphasis is on the  我 or I.