Can I sue a fast food restaurant if my purse was stolen there?

The business has no liability for a purse being snatched from you inside the business by a stranger to the business. You do need to protect yourself if your keys, home address, banking and credit/debit cards were in your purse. Change your locks at home. Notify your bank and everyone you had a card for in your purse. Not just the credit cards, but store specific cards as well. Have the accounts closed and new accounts opened. Ask the bank to not link the accounts together, especially if your online codes were in your purse or easily guessed, i.e. your DOB on your license or weak codes like 123456 or password or your last name.