Going to Italy for 3 weeks and my first time traveling alone abroad! Recommendations for how much $ to have available for 20 days....not including my rentals/hotels. Going to Rome, Positano, Siena, Cinque Terre and Florence. Is $100-150/day reasonable? I am a very light eater and don't plan on doing much shopping and will visit some of the sites ,but not interested in spending entire days sightseeing (ie. museums, historical,etc). I am doing all on train so I know I will need to budget train fare for trip days.
Also, how much to take in Euros (exchange here in US) for first day arriving and advice of how much to carry around when I am out and about. I have one bank account (Wells Fargo) and one credit card.