September in Cuba is very hot and humid, exhaustingly so for me, and when I was there, sunny every day. Havana is particularly hot if you do not spend time at the local beach. Not all cars or restaurants/bars have ac. But the atmosphere and the music are exciting. Hotels are not good value and casas particulares can be basic (but with ac) because of lack of options for certain items. The beach at Vedado (2.5 to 3/5 hours from Havana) reminded me of Tulum a bit (long stretch of white sand and turquoise water), but more commercially touristy with big resorts and their frequenters. Haven't been to the resorts in the cayos, but they are exclusively resorts, no locals; even the staff commute. The local Havana beaches were OK ,in Guanabo, lots of construction and other debris to cross to get to the beach itself and nice water. You can also get a day pass to a hotel pool.
In the Yucatan, we have always rented a car with ac, so we have some relief from the heat in the interior after touring a ruin. We have had no rain in September, although the forecast beforehand said differently. Lots to see. We usually do some sightseeing in the mornings and find a cenote or beach for the afternoon. Lots of charming posadas to stay at. For a week, you could make a circle from the airport to Valladolid and the ruins at CI and Ek Balam, maybe add Merida and the Ruta Puuc, and head for Tulum via Coba. The problem with many beaches there right now is heavy sargassum (not near Merida though).
I now have made friends in both places, Maya locals in Tulum and warm, wonderful Cubans in Havana, who we keep on touch with between trips.