This May we'll be spending a night in central Milan before renting a car to drive to Genoa. Would it be a good idea to take a taxi to the airport or train station and rent a car from there? Or is there somewhere else that's a good place to rent a car? We drove once in central Florence (a hair-raising, teeth-gnashing experience), and are afraid it's that way in all of the big Italian cities.
Are you going to take so much luggage to make a train impractical. It would be very easy to take the Malpensa Express from Cordona Station to Malpensa Airport and pick up your rental car there (although there will probably be an airport surcharge for pick up.) Malpensa is out in the country and very easy to reach the Autostrada from.
Denise, it is almost always cheaper to rent a car from a non-airport or train station location. There are extra fees tacked on to the cost at those locations. This is true just about everywhere in the world.
However, the selection of cars is MUCH better at the airports than elsewhere, especially if they can't give you the exact kind of car you requested. You're more likely to end up with something that will just barely be able to keep up with the fast-ish cars on the highway unless you get something at the airport.
Whenever I've rented a car in Europe I've never chosen the airport for pickup. But dropoff is fine at an airport, and often very convenient. If you go to Hertz or Avis or which ever rental place you're thinking of, you'll be able to select a specific pickup location. Just use google maps to map the location, and cross reference with a public transportation map of Milan. You'll be able to use public transportation to get to most locations.