Bypass San José?
OK. So San José isn't necessarily the Costa Rica you came to see. Those beaches and rain forests beckon, after all. If that is, indeed, the case, you can avoid the city altogether.
The international airport actually lies just outside the city of Alajuela, about 30 minutes northwest of the capital. Look for lodgings in Alajuela, San Antonio de Belén, Escazú, or Santa Ana—all within striking distance of the airport. Or head west.
Few international flights arrive in the morning, but they do exist, especially via Miami. Get here early, and you can head out of town immediately.
A third option is to join the growing number of visitors flying into Daniel Oduber International Airport in Liberia, where Costa Rica's northern and western reaches (including the North Pacific) are at your fingertips.