When I first placed the table and chair, the mayor was able to sit in the chair the same way as the benches. The next attempt to have the mayor sit in the chair resulted in yellow ring around the chair and the mayor standing next to it. Is this a bug?

Did you click exactly on the chair, or did you click right next to it? Accidentally clicking next to something when you try to click on it is a common mistake.

I clicked directly on it. It worked the first time but not subsequent times with any of the four chairs I placed. I have no problems sitting on the benches that I plcaed around town. After all that running she gets tired and needs to rest and relax.

I've seen this happen before too. I don't remember if I placed anything in the scene between the first time I tried to place the mayor in the chair and the second. I do remember that in one case the mayor would not sit down and later would. The game's idea of when a scene is too crowded for another element may be a bit fluid, or might be related to your zoom level or something changeable like how many bugs or NPCs are in the scene. I am just guessing here.