I suspect that your problem is not being caused by an LC voltage spike (if it was, the symptom would be problems with your load and you would want to put your capacitor on the other side of the switch as close to your load as possible). Rather, it sounds like your CFL transformer is drawing a large initial burst of current, which is straining your power supply and causing voltage to drop and your computer to reset. In that case, putting a large capacitor on the supply side of the switch (where you have it in your diagram) can help. I think you should try a larger capacitor; if you continue to have problems, you probably need a more powerful power supply.
By the way, just so there is no misunderstanding, is the 1mF in your diagram referring to milli- or microfarad? I have seen microfarad represented as mF before, and larger capacitors are typically represented in units of microfarads (e.g. 2200uF).