General Peace:
* Kapayapaan (formal)
* Katahimikan (more literal meaning of "silence" but can also mean peace)
Peace as in "be at peace":
* Magkaroon ng kapayapaan (have peace)
* Maging mapayapa (be peaceful)
Peace as in "goodbye":
* Paalam (this is the most common way to say goodbye)
* Makakapagpahinga ka na (you can rest now)
Peace as in "peace be with you":
* Nawa'y sumainyo ang kapayapaan (may peace be with you)
The best translation will depend on the specific situation you are in.