Sadly the answer is not a heck of a lot… There is sim390, which is geared to running the MUSIC/SP operating system, however the author died a few years ago, and it seems that there will not be any more releases, nor any source release.
There is also this old program, PC/370. And it provides an environment much like DOSBox, in that it traps and emulates MVS OS calls, and executes mainframe code on your PC!
PC/370 is old though, the last version was released around 1988! However it’ll run on dosbox just fine, and FAST too! I was clocking over 6million operations a second on one of the benchmarks!
While also looking around at PC/370, I came across this site, which includes a full PDF copy of the book “Mainframe Assembler Programming”. Special thanks goes to Bill Qualls for making this great resource available!
A neat feature of PC/370 is that you can use the PC graphic modes… like the simple demo plot XY…
Anyways, that’s about it!