Click for fullscreen. The data are from 2007.
One of many interesting interactive maps at MeasureofAmerica.org.
Addendum: I knew when I posted this that the display of the data was somewhat misleading, because SAT test-taking is not uniform from state to state, but I didn't have a link to clarify that point. I appreciate the efforts of Bill Hunt, who (see the comments thread) tracked down the aforementioned data on participation rates and the College Board's recommendations re how such data should (or should not) be used:
The SAT is a strong indicator of trends in the college-bound population, but it should never be used alone for such comparisons because demographics and other nonschool factors can have a strong effect on scores. If ranked, schools and states that encourage students to apply to college may be penalized because scores tend to decline with a rise in percentage of test-takers.