All Vaishnavite temples I have been to - the deity is called something other than "Vishnu", like "ranganatha" or "Venkatachalapati".
Yes, it is at Gaya in Bihar where it is called Vishnu pad temple. It is claimed that the foot print of Lord Vishnu on stone is kept inside of the temple. Gaya is an ancient place for worshiping ancestors. People from all over the world go there for giving 'pind-dan' for their pitar.
Yes, there are quite a few Vishnu temples in Kerala, where the presiding deity is simply "Vishnu". The most famous of them are a part of the 5 Vishnu temples built by Pandavas (one each), but it can be argued that the deity is Lord Krishna, even though the name goes by Maha Vishnu temple. However, the presiding deity of the Thirunelli Vishnu Temple can be clearly mentioned as Lord Vishnu.
Once when Lord Brahma while traversing the world, saw an idol of Lord Vishnu resting on an amla tree in the valley and thus the place came to be named Thirunelli. In Padma Purana (written by Veda Vyasa) there is mention of a beautiful Vishnu temple located in the picturesque Sahya valley deep in the middle of the forest. Thirunelli temple is also referred to as Amalaka temple and Sidha temple.