Can I use location services to prove I was in a certain location on a certain date

If you're looking for a previous date you can go to Settings > Privacy > Location Services > System Services > Significant Locations and look at the History. It will not show everything and it's not sorted by date so you would need to know where you were on a specific date and see if it matches up. I have no idea whether or not data from this would hold up in a court of law though.

You could do it by taking a "selfie" of yourself.

That "selfie" would be tagged with a date, time and location if you enable all these things under Settings > Privacy.

If this is a legal matter, I suggest consulting an attorney.