Most people (you included) will set about tidying a room at a time, often starting with the wrong rooms. The problem is that if someone turns up before you have finished the rooms they will go into, it just looks like you have a untidy house.
Further than that, what are they coming around for? Very few people will come around that will need to go into every room in your house.
If they are just coming for afternoon tea, what will they experience in your house? Probably the hall, one other room, maybe the kitchen and possibly the bathroom. They will probably not open cupboards or closets but will definitely come into contact with a tea cup, sugar, milk (I know you go all out with your tea set) and a plate for biscuits.
If I were strapped for time, I could combine this with Story Mapping to reveal what the minimum amount of tidying might be. If you are short of time, this allows you to focus your efforts on what is absolutely required.
Since we know the customer is going to require tea, we sort that out first. We make sure it's all clean and we have all the ingredients for tea (don't know about you but we always seem to be low on milk). Since this is the focus of the visit, it's the most important part of your guests visit. You can always cover, with "Sooo sorry about the mess, the grand kids have just left...." or similar if they arrive early and you have not finished the cleaning.
Next, we could start to clean the floors, again following the guests movements. We might notice that some things don't quite look right and we just sort those things right away. If they only take few seconds then it's worth doing there and then - we always try to leave a space better than we found it, as long as it makes our guests experience better.
Once you have your basic tea time experience nailed, you can think about those other rooms.
This focused way of thinking is what we would call a vertical slice. At any point, once I complete everything for a vertical slice I an review what is left and decide if I need to do the others or if what I have is good enough.