It is hot in Mexico in October even first thing in the morning. An umbrella is so great. It is like have portable shade. It is magically 10 degrees cooler. An umbrella can also be used to keep rain off of you. Shocking I know. When it rains people run to the building and leave you alone walking the site. Mayan ruins right after a rain are empty and amazing. I have used an umbrella all over the world. Find a good, but not too compact one and bring it with you.
All that being said Chichen Itza, even with the crowds, is AMAZING. El Castillo (the main pyramid) is truly a great site. Sadly, in 2006 they stopped letting people climb it as it was being damaged. Conversely pictures of the pyramid people free is awesome. This is one of the Seven Wonders of the World and is totally worth seeing. Stay in Valladolid and arrive early November to March would be better months to visit. And Rule # 1 applies in Mexico too. People are amazing. We walked to of our hotel and grabbed a cab to Ek Balam. We of course asked the price first. Cien Pesos, and he pointed at each of us. One Hundred pesos each, cool. We drove out to the site and I handed him 250 pesos. He looked at me funny and then handed me back 150 pesos. “Cien pesos por dos persones”. An honest taxi driver. I still tipped him 50 pesos with a Muchas Gracias. That is Rule # 1 People really are great all over the world.
In Venice, We geared up our rain suits and headed out into the amazing city. It was pouring. I have a great rain suit and shoes, but holy cow was it raining. I bought two umbrellas for 5 Euro each. What a difference! It only rained for an hour but the umbrella worked great. We kept these umbrellas for 3 months and used them for shade and rain defense. The only time they did work was when we left them in Split Croatia. I had to run 100 meters to get tickets in a pouring rain; the umbrella was left behind.
It rained in Olympia; it rained in Mystras. A good compact umbrella is always on my list.