The linga here was consecrated by mixing the sand with nectar of immortality by Shiva himself. There is a place to sit and meditate. You can go into meditative states here effortlessly.
How to get there:
The temple is located at center of Kumbakonam.
Map: https://goo.gl/maps/qChxrypnjpdYSEed8
About Kumbeswarar Linga
The legend has that there was time the entire universe was predestined to deluge. Lord Brahma secured the essentials of creation along with the nectar of immortality in a pot, kept it safely on atop the hill situated here. At the time of deluge, the water swamped the whole area and the pot was floated for some time and finally settled in a sacred land came to known to as Kumbakonam/Kudamukku. Lord Shiva shot an arrow on the pot and the nectar of immortality stretched all over the place, a Linga was consecrated out of this sand and remained here as Adi Kumbeswarar.
Source:
http://indiatempletour.blogspot.com/2013/01/pradosham-on-24th-january-2013-275.html
https://en.wikipedia.org/wiki/Adi_Kumbeswarar_Temple,_Kumbakonam