I'm planning for a trip to visit major Shiva temples in Karnataka. I have done some research and there are close to 54 prominent ones. Which are the ones which holds much importance in Puranas or mentioned in the Veda Puranas ?
AtmaLinga at Gokarna (It's an ancient temple, this AtmaLinga was given by Lord Shiva to Ravana at Kailash, but ended up at Gokarna due to Lord Ganesh's wit).
Manjunatheshwar at Dharmasthala.
Kotilingeswara nearby Kolar.
Chandramauleeswara near Sri Krishna mutt at Udupi.
Will update the list as I come across more.
Gokarna in Uttar Kannada district is one of the very famous temples which is mentioned in the Puranas. The main deity of Mahabaleshwara is said to be an atma linga of Lord Shiva.
Ravana performed deep penance in worship of Shiva, on behalf of his mother Kaikesi. Shiva was pleased with this and granted him the atma linga, but on one condition that if he keeps it anywhere on earth, the linga would get embedded in that place. Ravana agreed to this and started walking back home with the atma linga. Vishnu came to know about this and decided that if Ravana managed to take the atmalinga back home and worship it daily, he'd become very powerful. To avoid this, he came up with a plan to create a fake sunset, so that Ravana would need to keep the atma linga down, to perform sandhyavandana. Ravana was passing through the city of Gokarna at that time. Vishnu sent Ganesha disguised as a small boy. The plan worked, and Ravana then handed over the atma linga to the small boy asking him to keep it safely until he came back from sandhyavandana. Ganesha, however kept the atma linga on the ground on the pretext that it was too heavy. Ravana then tried to apply all his strength to shake the atma linga off its base, but the atma linga didn't move an inch. This was the reason why the name of the atma linga there is called Mahabaleshwara.
You can read the entire legend on Wikipedia.
Mention in the Puranas
Gokarna has been mentioned quite a lot of times in the Puranas, few of the references in Puranas are:
In the story of Binduga (Chapter 3 in the Glory of Shiv Purana), Binduga's wife Chanchula meets the intelligent Brahmin teacher (who brought her out of her miseries) in Gokarna.
Due to divine intercession it chanced that on an auspicious occasion she happened to go to the Gokarna temple in the company of her kinsmen
The story of Narada and the Champak tree mentioned in the Shiva Purana takes place at the Gokarna temple
In the holy teertha of Gokarna there was a temple dedicated to Lord Shiva. Narada once decided to visit this temple.
According to Bhagavatha Purana, Lord Balarama visits Gokarna during one of his piligrimages
The Supreme Lord thereupon traveled through Kerala and Trigarta and arrived at Gokarna, a place sacred because of the manifestation of Dhûrjathi, S'iva.