Can anyone help with ideas of what to see in Split Croatia and also Mykonos in early November?
Just about every town/city of an size has a website that gives you much more information than you get here. This is one for Split:
http://www.croatiatraveller.com/central%20dalmatia/Split.htm
Split has several well known sights, Diocletians Palace being the most prominent. There is also Trogir and Hvar close by. Mykonos, the town is neat and the island of Delos is close by. For both, Mykonos more so than Split, November is "out of season" so some stores and restaurants may be winding down. It may be too cold for beach time, a big draw for both areas, and the crowds will be subdued...which can be good...or a bit boring. Not sure how you are getting between the two, if they are stops on a cruise, then it should work well, if you are travelling independently, then realize it is not easy or cheap to get between the two.