I would suggest different resorts in different parts of the country, and two weeks rather than one. If you have never been to Italy, I would suggest making at least a couple of days for Rome, and I would also add Venice and Florence.
I would suggest one timeshare week be in Venice, if you can get a week there, but that is a really tough exchange. If you want to go to the beach while in the old city, simply take vaporetto (water bus) 1 or 2 to Lido, which is Venice's stretch of Adriatic Sea beach.
Exploring Tuscany is also great, but that is another rather tough exchange, and most of the resorts are inland.