Hi Amber Netherton,

create new report (not report type, just new report), select the report you are looking for accounts, then filter by selecting the drop-down arrow next to add, check cross filter, then select your main object in this accounts) without activities, then select add activities filter, then select status equals open. Please find the below picture is what you're looking for. Change your date field filters and off you go!

Hope this helps you

Thank you .