Depending on your speed, budget, and navigational sense, taxis and rental cars are good options to public transportation in Quito. Yellow taxis are ubiquitous, and all of them are required to use a taximeter. Though most of them do, some will not and you should expect to negotiate a price before setting off--it will be next to impossible to negotiate with the driver once he's started. Most taxi rides in Quito should cost between 1 and 5 U.S. Dollars, including the ride from the airport. Pay no more than double this for a ride at night. Hail or call a taxi as you would in the States.

Renting a taxi for the day or several hours can sometimes be a more affordable option than a rental car--most hotels can arrange for this service. Some taxi companies and services include Central Radio Taxis (2500600), Teletaxi (2220800\2222222), Co-op de taxis Brasilia (2550493), California (2400411), Colón (2543071), El Rosario (2533878, 2531578).

Quito has plenty of the big-name car rental companies available to book any kind of service from a 4x4 to a limo, and the rental process is similar to America's: you need to be at least 25 years old, hold a driver's license, and have a credit card. In Ecuador, however, there is no CDW (Collision Damage Waiver), and 10% tax and insurance coverage are extra. Further, you'll be asked to put around USD 2,000 on your credit card to guarantee the rental, and you'll be refunded the difference after you turn in the car. Also, most cars rented in Ecuador are manual transmission. 

Finally, look for a good car-jack in your rental; roads are in bad shape and you can expect to lose/deflate a tire at least once. But don't let that stop you from the adventure of Ecuadorian driving!