So, is there any handy way to simulate / debug Ethereum's OPCODES execution?
There are IDEs like Remix and Ethereum Studio but I don't think they have features designed around writing raw EVM opcodes. Code is written in Solidity and the compiled EVM opcodes can be traced through and debugged.
Here's an example in browser-solidity:
Click "Create", then "greet", then the bug icon near greet's result. Now click on "Instructions" and you'll see the following and can use the scroller below "Transaction" to step through each opcode.