It's been my experience that the Phillips gets some of the best exhibits that hit DC, including the spectacular Miro and Calder exhibit that just recently left.
They generally change the special exhibits every few months and advertise on their website and all over the metro. Unfortunately, it is usually an expensive admission, $13 last time I checked, or $11 if you're a student. Pretty hefty compared to the Smithsonians.
Also, even though the audio guides are free, you might be better without them, the people on the Calder/Miro exhibit's audioguides were pretty ineffective.
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