Yes, there are quite a few! Nothing west of Stirling, but in the Stirling area, Cambusbarron and the middle adit at Craigend Lime Works, also an adit at Murrayshall had become partly uncovered last time I was there.
Going south from there, it would be surprising if there were no workings at Fankerton, west of Denny, as the Murrayshall Limestone is known to outcrop in that region. Careful exploration may find some that we did not know about.
Going east, there is Bowden Hill, south of Linlithgow, various workings including Silver, coal and limestone in the Cairnpapple region, and extensive workings between Linlithgow and the Riccarton Hills. Going north you have the fireclay mine at Birkhill. East from there, I have heard that at least one oil shale mine may be accessible.
That is from memory, I think there are more, some that we know, and others awaiting rediscovery.
The Central Belt of Scotland is a great place to go for a looooooong holiday, if you are into the general purposes of this forum! I grew up there and never managed to see more than a small fraction of what is known to exist. No internet in the 1960s, alas!
North of the river you also have the small scale copper, cobalt, silver and calcite mines in the Ochils, and in Clackmannanshire some Limestone workings around Vicar's Bridge, then going east into Fife there are some impressive limestone mines.