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Mt Pleasant Library
This is one of the city's loveliest libraries, the third oldest in the city 1925, built in the Italian Renaissance style.
In addition to the cafes/coffeeshops above, the Mt Pleasant Branch Library is a great place to surf the web on the public terminals or the free Wifi:
While popular as a destination, this part of town is tricky with regards to crime. All three neighborhoods have very serious problems with muggings. Adams Morgan, contrary to popular wisdom, has not become safer "due to gentrification" violent crime has held fairly steady over the past several decades so you should take extra precautions when visiting. Muggings happen almost always on quiet side streets, so simply restricting your walks to the main streets will keep you safe, as will traveling in groups of three or more if you do need to navigate the residential areas at night.
Pickpocketing, a crime very rare throughout D.C., and indeed the whole United States, is rampant on 18th St at night on the weekend. Immense crowds of drunk people bumping into each other makes for a pickpocketing bonanza.