I have a few Ideas for the Toscany period:
3. San Gimignano - a must place, if you are in the area
I would not go to Genova. It's much more an industrial place. It has it's museums, churched etc. , but I must say I enjoined there the least.
Another nice place I found in Liguria was Campo Ligure but this is relevant if you are already close.
[ Edit: Sorry, no promos please. ]