is this your first time? if so, i would go to rome and one other city (florence, venice). that is plenty for a week allowing for some down time. 3-4 days per city including travel time between cities. the rest is based on how i like to travel. i like to "live" in the city so i do 1-1.5 intensive sightseeing day(s) then pick a different area each day to just explore --find the best gelato, chase down an obscure bookstore or boutique or see a special exhibit or pop-up restaurant, have a shopping/cooking/history lesson, people watch. or i pick an area each day and organize sight seeing / gelato / meals / coffee/shopping in that area, rather than rushing from place to place. eventually, i get churched-out--having a guide is a great idea, as is purchasing tickets ahead of time so you can skip the lines.
that said, i'm not fond of rome after you've seen the highlights. we did do a daytrip to pompeii, herculeneum would have been better but we ran out of time.
enjoyed florence with a day trip to pisa. venice was super--enjoyed the biennale.
i adored sicily--we drove from palermo to taormina immediately after we landed. took day trips from taormina and back in time for a great dinner. hiked etna, went to the beach, checked out syracusa. didn't make it to agrigento--next time. pace was slow, we didnt' rush, slept in when we wanted. very very chill.