I think people are thinking too small with placing the telescope next to a nearby solar system with possible life — while it might take us a few dozen decades we’ll eventually get there soon enough anyways. Plus we don’t really gain much information looking at a new solar system with just a single space telescope, we’ll need a proper full-decked out station and everything.

Rather, this telescope (assuming it can’t be placed on Earth and deconstructed to understand the technology of a magical FTL communication and transportation) should be used to actually advance our understanding of the universe in a way we will unlikely see anytime soon in the next hundreds and thousands of years.

Next to / in black holes, at galactic centers, above a galactic plane, and at the edge of the universe are all excellent choices.