Apartment Hunting on the weekend can be accomplished. There may be buildings that can't be entered because the management companies where the keys are kept aren't available, or worse yet, it may have been rented on a Friday and you won't know until Monday whether it was available. You're probably better off leaving Thursday night, start early Friday, and leave Saturday night.
You may also want to fill out the form located at:
https://www.bostonapartments.com/findapt.htm