The first place to start looking is the employee handbook. That will let you know what they do with leftover vacation and sick leave. It can even depend on your jurisdiction. Some companies have to address issues like this differently for different groups of employees depending on which states laws apply.
Generally they want you to work every day during the notice period. It is for you to document and train, and for you to finish some of the open tasks. They are expecting this.
If they don't pay you for unused sick leave, but do pay for unused vacation; they may be very strict about documenting an illness during your notice period.
The determination of the last day is very important when planning the transition to your new job. How the old company handles things like vacation, sick and insurance is very important to know.
While a check for unused vacation is great, if it comes with the expense of being uninsured during that time period you may want to wait until you come back before resigning. Of course if the insurance coverage carries over till the end of the month...then taking a break after your last day of work may be relaxing.