In every village in Tamil Nadu, it is common to find a Shiva temple, a Vishnu temple and the gramadevata temple. There will be many other temples too, of course - dedicated to Ganesha, Muruga, and so on - some with historical significance and some that have just come up as a result of devotees' desire to see one in their neighbourhood.
So, when visiting a place, it is up to us to choose to go to 1, 2 all 3 main temples based on our family's belief system. For instance, if you go to Kumbakonam, you have the Kumbeshwara temple dedicated to Lord Shiva, and Chakrapani, Sarangapani, and Ramaswamy temples for Vishnu. Uppiliappan is normally our first destination as He is our family deity. In Srirangam, there is the Vishnu temple that cannot be missed and Thiruvanaikkaval Shiva temple nearby is equally famous.
One may say, how does it matter who the presiding deity is. A temple is a place of worship and our prayers is all that matters. I beg to disagree. There is a subtle difference in the energy one feels in each temple. In Siva temple, there is no form to distract us, only a lingam to represent the infinite. It is more subtle, more meditative, more calm.
In Vishnu temples, the deity is more resplendent, bedecked in jewels, with his consorts by his side and other devatas too surrounding Him, depending on the kshetra. Here, with the sanctified water and sadari, the devotee gets more than mere darshan. The lure is His beauty that captivates and binds us to Him in a different way.