European MMS hotels aren't quoting VAT on the search results page. You see it added well before booking, but when searching in Europe MMS looks cheaper at first glance.

"lowest cost" isn't really the right search IMO. What you really want is "no more expensive than other Hyatt options in the vicinity". You're hardly going to fly half way around the world for a "cheap" MMS hotel.

And, besides cost, I'd be focusing on places I'd like to visit where there aren't many other hotel options, but I can stay at an MMS and pick up the badge that way.