I'm not sure how the previous poster describes 'invasive' but I have never heard creeping thyme described that way. It does spread - that's what groundcovers do - but never to the point of being invasive. And it is a very good choice for areas that may be hot and dry and takes foot traffic well. I would also suggest considering rupturewort (Herniaria glabra), brass buttons (Leptinella squalida) or Corsican sandwort (Arenaria balearica), although the last two are not as drought tolerant as the first and would appreciate a bit of water during dry periods. These are all very low - almost flat - mat-like plants that work perfectly between pavers or flagstones.

Creeping sedums or stonecrops could work also but tend to be pretty succulent and will get damaged with much foot traffic, although they will bounce back rapidly.

By invasive, I mean that the groundcover moves rapidly into areas where I don't want it, and it's nearly impossible to eradicate.

All groundcovers will do that. That's why they're groundcovers! You have to remove them from the areas where you don't want them to spread.

Creeping thyme roots as it grows but it is not at all difficult to remove from where it's not wanted. And it is far less aggressive or difficult to remove than many, many others groundcovers.

I have never heard thyme described in this manner. It is also not the correct use for the term 'invasive'! That is used to describe non-native plants that take over or threaten native areas..........which thyme does not do.

I'm glad that you've had a better experience with it than I have.

What can thyme crowd out?

Why don't you want it in some places?

This might help choosing creeping thymehttps://theherbladyblog.wordpress.com/2017/03/20/my-thyme-garden/