*If he has an iphone and you can get it (I know what you said about him changing password but I'm thinking just ask to borrow it to google something as yours is out of power for example)
try this:
Settings >Privacy>Location Services
Scroll right to the bottom of the Location services screen
-->System Services (its the very last item at the bottom)
At the bottom of the first section (above the grey bar that says Product improvement) is Frequent Locations
Tap on that and if it is turned on, you will see a history of places visited regularly.
Two things to say about this:
I know it sounds like a lot of nested links but if you know what you are looking for you can do this in a matter of seconds. Try it a couple of times on your own phone and you'll see once you know where everything is.
Plenty of people who are super privacy conscious don't realise there is this frequent locations function and so haven't turned it off.
*Beyond that if you are set on catching him out, either a private detective or get him to commit to a location and then cross check.
For example, if he says he is working late, turn up at his work with a ready excuse for any staff - "we planned to for dinner and he's not answering his phone". If he says he is at a works drink, go and see whether he is there.
You need to be very careful with the latter though because you can only do this once or max twice (if you are seen or identifying yourself to staff at his work) without looking like a stalker so you need to pick your time carefully based on his previous behaviour.
- Or you could turn on find my iphone on your phone if you have it and put it in his brief case or bag or car. Then log on to icloud and find your phone. It will show you where your phone is - which may not be the same as where he is precisely but could be.
Only cast iron way to catch him though is to follow him until he meets relevant woman.