We will be arriving two and a half days early in Palermo for a RS tour of Sicily in March. Any suggestions for nearby sightseeing which will not be included in the tour? We could rent a car if needed, but would prefer train or bus.
Not sure what the tour covers, but I'm willing to bet you can use the extra days just in Palermo or nearby beach (Mondello). Check out Tripadvisor's Things to Do for Palermo - there is a cool, but gorey Cappucchin catacombs for example (not for everyone, but really interesting).
http://www.palermocatacombs.com/
http://www.tripadvisor.com/Attractions-g187890-Activities-Palermo_Province_of_Palermo_Sicily.html
The Palatine Chapel is lovely and I don't see it on the itinerary. Very near it are the ruins of the San Giovanni degli Eremiti monastery with cloister. Try to find out from RS if these are included in the walking tour. There is a puppet museum (you'll see a puppet show in Siracusa).
The tour doesn't go to Cefalu, so I suggest you spend 1-2 nights there before the tour.
Another vote for Cefalu.
I just looked on the schedule (I assume it's the off-season tour) and it seems that the tour basically uses Palermo as a flying gateway but only spends a few hours touring there (after Monreale) and then leaves it to you for the rest of the day. That is no way enough time in Palermo especially if the afternoon timeframe only allows you to see one attraction due to closing hours. I would personally spend your extra time exploring there instead of heading elsewhere. Your first day will be probably marked by jetlag so better to just ease into your trip instead of heading out somewhere else (Cefalu is lovely but frankly Palermo has more sites and a different, more chaotic feel that's very Italian and should be experienced).