BeccaD:
I would never tell someone not to go anywhere in Greece be it Santorini or elsewhere. Everyone has their own opinion of what they want for a Greek Island and/or Mainland Experience. First timers usually get influenced by travel magazines, travel agents, web sites, etc. about an island like Santorini. It does have spectacular scenery and "looks" Greek.
My favorite Greek Islands are Sifnos, Milos, Naxos, Amorgos, Astypalea, Tinos with Tinos turning out to be a gem of an island. Astypalea has in my opinion the most beautiful Chora, Sifnos is starting to gain popularity but still is Greek, Milos is nice, Naxos is a wonderful combination of Old & New World Greece.
Numerous other lesser- known islands: Ikaria, Fourni, the Small Cyclades, Skyros, Kythira, etc. Don't overlook the mainland, especially the Peloponesse Peninsula, especially Nafplio, one of Greece's loveliest towns and close to World Class Archeological Sites.
I would recommend the Blue Guide to the Aegean Islands, Greek Island Hopping for guide books and check out Matt's Greek Guide for everything on Greece:
http://www.greecetravel.com/
In the end you are the one to make a decision. Do your research and ask questions. Greece is a wonderful country filled with history, kind, courteous and passionate people and some of the best food in the world and the prices are more than reasonable.
You'll find September an ideal time to be in Greece . . . off season, less tourists, low prices and still nice weather.