i think your itinerary looks great but i have to say I'd skip the travel over to the east coast places you've mentioned (ancona, pescara, bari) as to be honest the beauty of those areas are not in the cities but in the villages around them. From Bari you can go to Alberobello and the amazing Trulli and Lecce is a gem. The coasts are spectacular and the villages stunning. I don't feel that you'd experience any of that by doing day stops in the cities mentioned so i'd recommend adding time to the other places on your list.
i'd say that you won't regret adding time to your travels in sicily as there is lots to see and agree that Taormina is a beautiful place. It is very pricey there but there is an excellent campsite just off the road that winds up to the village. The views are spectacular.
have a great time
Thanks for the kind wishes
The cities I listed on the East coast are just the major ones I intend on spending the night in. When I'm in Bari I intend on spending most of my time in nearby villages and historic sites, not the city or Bari itself. If I can find a cheap hostel in one of the scenic towns I'll stay there instead but for now, I'm assuming the cheapest rooms will be in the main cities (Either way I don't want to completely skip the East coast).