I once had a similar thought, but I wanted to use periodic comets to study the solar system, not the comet itfself. Once they reach the outer solar system, comets lose their tails (become inactive) and would be great platforms for telescopes and other stuff. Depending on the specific comets orbit, they e.g. pass outer planets, the Kuiper belt, or even the Oort cloud. You wouldn't have to care for propulsion and stuff; you'd use some type of nuclear energy instead of solar panels, and you're good to go ;-)