San Diego Metropolitan Transit System Route 992 bus offers a 20 minute trip to Downtown San Diego from Terminals 1 and 2 and the Commuter Terminal. The bus departs every 15 minutes between 5 am and 11:30 pm on weekdays, and every 30 minutes on weekends and holidays. Fares start at $2.25, but if you're taking the bus more than once, a Regional Multi-Day pass offers unlimited rides all day for $5.
The truly adventurous can bike or walk the 3-mile shared-use bicycle/pedestrian path connecting the airport to Little Italy and Downtown San Diego. Google Maps highlights the official path, which runs along the San Diego Bay Waterfront on one side and North Harbor Drive on the other.