My abusive sister finally made the mistake of beating the hell out of me and stealing my brand new iMac ALL IN FRONT OF WITNESSES. Is it legal for me to ask her to pay for my computer, I.e, pay restitution, and in exchange I won't go to the police?

Nope that is blackmail and will get you in jail. You may ask her to pay you back, you may sue her in civil court for the money or you may call the police.

The longer after the crime that you wait to call the police, the harder it will be to get it to go to court or charges pressed by the DA, The police will need to photo the injuries, and you should have documents of the medical bills of the injury.