Of the major JRPGs, the obvious SNES one is Final Fantasy VI/III, but my favourite is clearly Chrono Trigger, which is far more inventive and interesting than I was expecting. Front Mission is a Squaresoft tactics game which is lots of fun - turn-based, tile-based, much like early XCOMs - about piloting mechs. Only released in Japan, there are patched fan translations available, and you might enjoy that.
My secret favourite SNES game, though is Unirally/Uniracers, which is just fabulous and fast/fun.
There's not a lot of turn-based strategy on these, although you might find Herzog Zwei on the Megadrive fascinating - a very early stab at what we'd now call RTS.