Present day Hampi, is said to be Kishkinta. So if, Sita Devi had been abducted by Ravana, then It logically hold good, when Rama, as instructed by Jatayu, walks down south via Hampi, partners with Sugreevan and slays Ravana. According to this Citrakutam should be in North.
But, Rama has performed 'Tharpanam' for Jatayu at Vaidheeshwaran Koil. So, the fight between Jatayu and Ravana may have been near this town. And this holy town is still south of Kishkinta/Hampi, could not be where Jatayu was slain. Or did Rama perform 'Tharpanam' at some other day like Mahalaya Paksham?