September is in the hurricane season. But are there parts of Mexico that are pretty much hurricane free and have sunny weather (I want to spend the days on the beach) during that month?
Usually the Pacific side is OK, it's just the Atlantic side that gets hit hard (again, usually). Puerto Vallarta is a popular spot on the Pacific side.
Hope that helps.
I'm currently in Mexico, on the Pacific side, during hurricane season.
If you want sun it's hard to beat Baja Sur (southern Baja). There is little rain unless a cyclone comes through, and the sun and heat are punishing to say the least.
The weather on the mainland in the peak of summer (August/September) is hot, muggy, wet, and bug ridden. Baja is also pretty bad but minus a lot of the moisture.
I honestly don't know anyone who's spent August and September in Mexico that would voluntarily do it again. The weather is pretty bad, you'll hide in an AC'd room as much as you can, and cyclones can affect you anywhere.