I spent about that much time in Naples and Salerno (and the AC), but in February when it wasn't crowded. From Naples you can visit Ischia if you want an island. Naples is sort of Rome on steroids without the amazing architecture. As one of our old forum members loved to say - the only subtle thing about Naples is its charm. There are some wonderful things to see, interesting places to explore, great food and an excellent archaeology museum. You can also visit Pompeii and other ruins easily taking the local Circumvesuviani train.
I love Salerno. It is connected to Naples (and rome if that's your gateway) by high-speed train. It's also the eastern terminus for the bus line to Amalfi town and the various ferries that sail the AC coast. Among other attributes, Salerno has a well-preserved historic center and a large sandy beach (I believe it's the only one on the AC - most towns have small, generally pebbly ones). A bonus for the budget is that both rooms and restaurants are cheaper than in the AC villages. You can spend days hiking the coast and then have a swim and a great dinner back in Salerno.
PS - be sure to stop at Sal de Riso in Minori. Their pastries are to die for. I'm told the gelato is exceptional but after a pastry I was so sated, I couldn't even bring myself to taste it :-)
Sicily needs at least that much time. It's the biggest island in the Med and there is so much to see and do.
