So sorry you are going through this OP. I caught my DH out with an OW last year, and ended up spending about 6 weeks gathering evidence and getting my ducks in a row before I confronted him. He tried to deny things for quite a while, even when it was clear we both knew he was lying. I think he thought a lot of what I was telling him I knew was guesswork, eventually he realised I wasn't guessing and admitted it, but it took a while even after that for him to admit the full extent if what had been going on. I think in his head he thought he could limit the damage. Like you, I had my suspicions, (without any evidence), and he'd denied it when I'd asked him a few months earlier.
it was incredibly difficult carrying on as normal, but it was definitely worth it because he didn't get chance to cover his tracks and I also unearthed a few other shitty things he'd been doing that affected me and the DC, and I might otherwise never have known about thanks to his damage limitation attempts.
You may be able to find out a rough idea of the address with a bit of detective work of your own:
If you can access find my iPhone you can keep track of where he goes.
If he has an iPhone and you can get into it, look in Settings / privacy / location services / system services / frequent locations. This will give you a list if places he often goes.
If you can do either of the above, using google earth will give you a street view of the area which may also help. I was able to narrow it down to an apartment block this way.
A lot of people on here will assume you are of course going to LTB, but If you do decide to try and work things out (we have, though the affair had 'only' been going on for about 6 months and turned out to be a slightly bizarre 'sex only' situation), then it will be a long and difficult journey to which you both need to be 100% committed. Having couples therapy with a really good counsellor is getting us there, I don't think we would have been able to get this far without it.
Thinking of you, you're in shock and you must be going through hell right now, but it does get better eventually.