We , family of 4, are traveling from Venice to Florence to Rome to Naples in July. 3 nights at each city. Any recommendations on booking. Does italy use Uber in town for short trips to dinner or sightseeing?

Ubers are not in Italy at all. Taxi are the best bet for short trips. Just make sure you use a government taxi and not a private one. The government taxis are all white with a sticker on the side. They are at taxi stands all over each city and will not stop if you try to hail. 

There are Ubers in Rome, I used one, but their rates are not always better than taxis.  I tried to get one and the price quote was 40 Euros but we got a taxi instead and it was only 15 Euro.  Taxis are plentiful and you can download the ItTaxi app which I found useful for booking future rides.  Enjoy your trip.