There were several monuments at the site in antiquity, but as it happens, the Pausanias passage you're thinking of (Pausanias 3.14.1) is about a memorial in Sparta, over the remains of Leonidas which were transferred there in ca. 440 BCE.

As for memorials at Thermopylai: Herodotos 7.225 and 228 describes a memorial for Leonidas himself, a statue of a lion; and three inscriptions, one for the southern Greek army, one for the Spartans, and one for Megistias of Akarnania. But he places only the lion at the supposed site of the southern Greeks' last stand (I say "supposed" because a competing, and equally likely, version of the battle has it ending at the Persians'/northerners' encampment). Strabo 9.4.2 refers to five memorials at Thermopylai, one of them for the Lokrians. And Stephanos of Byzantium quotes an inscription dedicated to the Thespiaians.

If any of these memorials survived, it would certainly be of great cultural value, and potentially of some historical interest. But Thermopylai has had a rather active history: there have been many significant battles fought on the site since 480 BCE (including one in WWII, between the Germans and the ANZACs) -- all of them failed defences, incidentally: the place has a rotten history as a defensive point -- and in addition, the topography has changed a lot. The pass was once, of course, right on the shore of the Malian Gulf, but there's now a substantial region of farmland between the ex-pass and the shoreline. The hill of Kolonos is, I believe, popularly thought to be the site of the southern Greeks' last stand following the Herodotean account (though it's not actually certain, and as I mentioned, his account of the end of the battle may well be untrue), and some core samples have been taken there, and finds of quite a lot of arrowheads and spearheads; but no inscriptions.

As for the monument in Sparta mentioned by Pausanias: the remains of the Leonidaion still exist in downtown Sparti (not exactly in the park where there's a statue of Leonidas, but just round the corner), and you can visit if you wish.

Further reading:

• A classic article (PDF) on the topography of Thermopylai, details of the shoreline, and much more.
• Beyond the Gates of Fire (ed. C. Matthew and M. Trundle, 2013) has a chapter by one of the first article's authors, "The topography of the pass at Thermopylae ca. 480 BC", which retells and rephrases the same material for a slightly more popular audience
• In the same book, Trundle's chapter "Thermopylae" has some info about the memorials at the site: see pages 31-33. (He's mistaken about the last poem he quotes, an eight-line fragment by Simonides, but that doesn't have anything to do with the memorials so it doesn't really matter.)

Edit. Clarification, and added a couple of bits of bibliography