Light cycles are a time honored variation on Snake. That's a good start. If you have not played TRON 2.0, I suggest you check out the demo for some ideas on how to make the game more interesting. Slow/fast zones, obstacles, and powerup come immediately to mind.
Some other interesting effects might be jumps, bridges, or adding enemy units besides other lightcycles. Imagine grid bugs latching on to your jet wall and you have to shake them off your tail (either by evasive moves or running across and energy spike to send a charge down your line. Also, heavy 'boss' units like tanks and recognizers can lumber into the light cycle arena and break down walls or fire at you.
Lots of potential there, but you'll have to hussle to get things done in only one month.
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TAZ
"Do you think it is wise to provoke him?" "It's what I do." -- Stargate SG-1