Forget the travelers checks. Stick to using the ATMs for pocket money and use credit cards for big purchases. Get a CapitalOne card if you don't have one. They do not charge a foreign conversion fee (the only card I know of that doesn't). .
I bring only a limited amount of US$$$ to use in US airports and for transportation expenses.
Wait until you get to Rome to get your Euros. They are expensive to obtain here in the states and there are ATMs EVERYWHERE.
When are you going? I'm on the June 2 Mosaic with my granddaughter.
Sue