Rick has recently released his first guidebook to Sicily. I highly recommend it (sight unseen). For additional input you could look for a Lonely Planet and/or Rough guide. Old editions can be found online. There is much that I missed in Sicily.
Nights spent by location, with side-trips indicated:
Catania (6): Piazza Armerina (Villa Romana del Casale)/Caltagirone, Mt Etna/Taormina, Enna
Siracusa (4): Noto/Ispica/Modica, Scicli, Ragusa
Palermo (5): Monreale, Cefalu
Trapani (3): Erice, Egadi Islands
Messina (1): Positioning myself for bus to Puglia
The first day in Catania was wasted because I stupidly took the overnight train from Rome. The miserable, sleepless night meant I slept most of the next day, which of course produced jetlag-like results. I spent two days traveling from Catania into the interior; it would have been better to spend 3 nights there. Catania itself needs no more than one full day. It has a nice cathedral, an attractive historic area, and an interesting food market. Alas, I missed the WWII museum so can't tell you how much time that would call for.
I wished for one more night in Siracusa, because Ortygia (medieval center) is lovely, and I was just snatching an hour here and there to see it. Ragusa was my favorite of the Baroque towns (and the largest), but they're all worth visiting. I liked the archaeological museum and archaeological park in Siracusa, though they might pale for an aficionado after a visit to Agrigento.
Palermo is sight-rich, especially in terms of churches and chapels. Although I'm not religious at all, I went to many because there was a lot of architectural variety; their hours vary a lot. Monreale (just outside town) is an absolute must, and the in-town Capella Palatina is almost as spectacular. There are two good food markets and an archaeological museum. Palermo's a large city with a lot of ground to cover. Cefalu is a former fishing village, now beach resort. A few hours were enough for me, but others like it a lot more and enjoy spending a night or two there.
Trapani is attractive. I regretted devoting a day to the Egadi Islands. They're fine, but who needs uncrowded, sandy beaches when there are so many interesting places in Sicily? The medieval hill town of Erice is fabulous (expect the center to be very touristy during the middle of the day); it's reached by a funicular from an obscure part of Trapani, or there's bus service. I'd say Trapani is skippable, though nice. Erice is pretty special.
Messina has an old cathedral, but it's not really a recommended destination, given all that Sicily has to offer. I only went there to catch a bus to Lecce. I walked around for a couple of hours and nothing made me wish I were staying longer.
Only limited time led me to skip the Aeolian Islands, but who knows--I might have been underwhelmed by them as well.
I needed all the bases I had, and--as I wrote above--would have benefited from having an additional one in the interior. Train service is somewhat limited in Sicily in the sense that there's little service through the interior and the trains tend to be slow and infrequent. I ended up using a lot of buses (Palermo to Trapani is substantially faster by bus, though there is rail service), and they are not fast. There's also little if any town-to-town bus service on Sundays and holidays, so be very careful about that when you outline your itinerary. Also, there are school-day schedules and non-school-day schedules; good luck with that.
I found it not so easy to find Sicilian bus schedules online, so I just went to the bus station in each city, looked at posted schedules, and asked. Don't expect English to be spoken. The schedules obtained on the ground in Sicily seemed generally reliable, but there was one occasion when an extra bus showed up, so I suppose I might have been lucky that none of the ones I wanted went missing.