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A good starting place would be the rear of the moon. All that lovely rock would shield you from the radio noise of Earth. You'd get some awesome radio astronomy done there and could have a SETI environment as well.
Pluto would be perfect for an infrared imaging telescope. it's so cold on Pluto that you should be able to detect the faint heat coming from extrasolar planets and be able to analyse the atmosphere and, if it's big enough, directly image the planet.
Colder on the moon, is it not?