Calculating a room available days

Since you're trying to report on something that doesn't exist - you'll have to create something new that Quickbase can report on to isolate that type of information. I would recommend making a new table called 'Unit Days' or something like that. Its a child table to Units that really only needs 2 fields - the related Unit and a date field to designate the day. 

You essentially want each record to represent that specific day of the month in relation to that unit - so each unit has a record for each calendar day. You can manually import the records using excel and import the next 5 years worth if you want to have it all set up. 

Since you already have the reservations setup - the easiest option would be to use formula queries to check each of these unit days and evaluate if that day falls within an existing reservation. Your just querying to see if a reservation exists that starts on or before the unit day in question and ends on or after that day, and if a record exists you know it's occupied. 

Your reporting can really then be whatever you want it to be. You could make formula query response a text field for occupied / vacant, you could make it a checkbox to just be true false for reporting, whatever makes the most sense. Plot it on a calendar, table report, summary report etc.