Should we book hotels ahead of time, or would it be better to book as we go? We're staying in Italy 10 days and renting a car.
It depends on when you are going. If you are going during high season, definitely book ahead. However, if it's low season than you are fine booking as you go. Even then, I would recommend possibly having some backup hotels booked just in case. Many Italian hotels and b&bs on booking.com have a 24 hour cancellation policy.
My daughter and I once arrived in Venice without reservations. We parked in the large parking lot and called the "I". They told us the city was booked solid. So, we picked up Rick Steves' book and started calling places. We lucked out the second place we called, and after difficulty with them not speaking English, we got a room and then had a challenge finding it. However, after all that, I was a great place to stay and probably wasn't listed on the internet. Last time we went, last May, we booked ahead. Still had difficulty finding the hotel and the place wasn't as nice. Go figure. In the end, I would book.
If you are going to one of the very popular cities, in high season, definitely book ahead. This is especially necessary in Venice, or Florence anytime from June to September or Verona during Opera season. I wouldn't really recommend you stay in Venice or Florence though. It's often much more comfortable to stay in a town close by (Treviso or Padova or Venice, Bologna or Modena for Florence) you will avoid the crowds and can easily get to Venice or Florence by train for the day, leaving your rental car at the hotel, as parking can also be challenging in Venice or Florence. Outside of the high season and popular cities, booking hotels or B & Bs as you go should be fine. Try a site like Venere. Lovely driving routes for 10 days are Tuscany & Umbria or around the coast of Puglia.
Mentioned in this answer:
With very few exceptions, I'd recommend booking in advance - while in low season it is less risky to book upon arrival, Italy is so popular that there always some risk of remaining 'homeless'. Also, I would recommend researching any festivals or events happening in any particular Italian city or nearby town - to be sure you're a) not caught off guard or b) you don't miss out on a local, authentic event!
You should absolutely book Venice ahead of time. Central Venice is fairly small, and will get crowded fast. Many places have pretty friendly cancellation policies, but if you are renting a car staying in outer Venice might not be too bad
Yes! Ditto to the others who've commented here. It's better to book ahead than to find yourself without a place to stay. If you need flexibility, book with a place that gives you the free 24-cancellation option so that you can change it later.