1) zero-cost option:
a) You could use this:
in theory, it's supposed to fully emulate mega65 but there are still a few things missing.
b) download xilinx ISE and play with FPGA code - you can do quite a lot using just the ISE without even owning the Nexys-4 board
2) costly option
Buy a nexys-4 board - I assume you're still in school so you would qualify for a discount - the board might cost you about $150 (assuming you live in the U.S.).
Then you can play with full development on the actual hardware that's pretty close to what mega65 will run on.