Did you apply all software updates on your prior version prior to upgrading to Mavericks ? (Not sure if this is a necessity, just know that the one mac I've upgraded so far to Mavericks was completely updated prior and I've had no issues with Safari).
Have you tried repairing permissions ? (Applicatons -> Utilities -> Disk Utility -> Repair Permissions)
Have you checked if its a user profile issue ? (Create a new user in System Prefs, logout and login as the new user .... try Safari).