The Italians worship children no matter how noisy or messy. Jet2 flies to Pisa which is beautiful and connected by rail to Florence. Loads of rental properties in the area. The Turks are like the Italians on speed. No matter what kids do, they are adored. From Hisaronu you can do a number of trips such as the Dalyan river, a deserted Greek village or a boat trip. The water at Olu Deniz beach a few miles away is like sitting in a warm bath. Will send you a few more details later when I have time if you want but we would recommend the Asena Village Hotel in Hisaronu.
In Turkey http://www.caroletayfun.com/ did our tours. They pick you up from the hotel. http://www.asenavillage.com/ was where we stayed. I must warn you that Hisaronu is quite touristy although this hotel is about tenminutes walk out of town at the edge of a wood and so is much quieter.
For Italy http://www.jet2.com/ do flights to Pisa http://www.holiday-rentals.co.uk/ have holiday rentals
We stayed at http://www.holiday-rentals.co.uk/p649988a The family who ran it were lovely. It's not that far from a railway station where you can get trains to Florence and Pisa. Siena was our favourite city of all. Italian food is very child friendly. Pizza and pasta is always a hit and the icecream was delicious! You will be warmly welcomed when travelling in either Turkey or Italy with a baby, not just tolerated. Grown men will stop to admire your children who may be given perks such as icecream or cake for free. So different to the UK. This year on our second trip to Turkey, a mini bus driver altered his route to take us home when he saw that we had a four year old with us. sorry, just reread the grown men thing. Sounds creepy but it really isn't. They are not prededatory, they just adore all kids.