I'd like to add Cinque Terre and Lake Garda as a point of relaxation - so would like to find accomodation with pool or near to beach so we can relax a little, while the cities will be much more on the go. I was hoping the weather will be nice enough for swims etc, so would like a little longer in Cinque Terre and Lake Garda to do so
You'll be there September- October. Rome is roughly at the same latitude as Boston. Also, Lake Garda is polluted and swimming is not advised.
Your time in Italy is precious. There's so much culture and history to be explored I can't imagine spending most of what little time you have sitting on a beach or in a swimming pool. If you'd like to spend a day relaxing, natural hot springs might be an alternative, especially that time of year. Be aware the water is sulphurous and smells that way. You'll want to bring a bathing suit you don't mind throwing away at the end of the day. The springs are in Tuscany, roughly halfway between Siena and Rome.
The problem with CT, especially if you are using it to relax, is that if it gets cold and rainy, there's really nothing else to do. In cities like Florence you can easily change your plans to inside acitivities.