How do I determine the junction-to-ambient thermal resistance?
However, the datasheet doesn't tell me what the 
  thermal resistance is.


The thing about the published junction-to-ambient (θJA), it is only a reference used for comparison purposes.  You need to estimate the thermal resistance of Your PCB (θCA). The published θJA is based on the device being mounted on a JEDEC test fixture. 

This Texas Instrument App Note, Thermal Design By Insight,Not Hindsight, is very good and explains how to calculate θJA.

From page 3 of the app note:


  Use the value of θJA given in the data sheet to compare
  different packages, and use it along with the IC power dissipation for
  a sanity check in your design. The high thermal resistance of the
  plastic packaging ensures that most of the heat travels from the
  exposed copper pad to the PCB, which usually has a much lower thermal
  resistance. A heat sink can be added to either the top of the package
  or directly beneath the exposed pad on the backside of the PCB. Again,
  because of the high thermal resistance of plastic, a heatsink will be
  more effective when connected to an exposed metal pad, either directly
  or, through thermal vias.  
  
  Since most of the heat transfer is through the exposed pad to the PCB
  it becomes immediately apparent that the value of θJA is
  highly PCB dependent. In other words, the most critical value to
  determine in any design is thermal resistance of the PCB (θCA). Well
  what, exactly, is θCA and how is it calculated? θCA is the
  equivalent resistance of a thermal resistive lattice that centers on
  the IC and ends at the surfaces of the board. It is the final of your
  freshman year, Circuits 101 class, all over again. Figure 3 below
  shows the details.


  

UPDATE:

This document describes traditional and new thermal metrics and puts their application in perspective with respect to system level junction temperature estimation.

Semiconductor and IC Package Thermal Metrics