Kumbakonam is underrated among pilgrims. Many great shrines -
Darasuram
Sarangapani
Oppiliappan
Swamimalai
Rahu Sthalam (undervisited)
Nachiyar Koil
Adi Kumbeshwar
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It is a touristy place
Temples like the one in Swamimalai or the Oppiliappan shrine easily beat it hands down
For math enthusiasts, there is an additional pilgrimage a few blocks from Sarangapani temple - the house of Srinivasa Ramanujan, the place where he spent most of his childhood / adolescence