The four Dhams are not variations on one shrine. Each belongs to a different regional tradition with its own deity, its own liturgy and its own peculiarities, and the set is held together by geography and by the idea that completing it completes something.
Badrinath in the north, in the Garhwal Himalaya, is a Vishnu temple whose image is a black stone Shalagram form. Its head priest, the rawal, is by long convention a Nambudiri Brahmin from Kerala, at the opposite end of the subcontinent, an arrangement usually attributed to Shankara and remarkable for having held for centuries.
Puri in the east is the temple of Jagannath, and it is the one that most resists assimilation to standard Vaishnava practice. The deities are wooden, roughly carved, without hands or feet in the ordinary sense, and they are periodically replaced in the Nabakalebara, when new images are made from a specific kind of neem tree located by prescribed signs and the substance held to give them life is transferred at night by priests who are blindfolded. The Rath Yatra takes them out of the temple on enormous cars.
Rameswaram in the south is a Shiva jyotirlinga, connected in the Ramayana to Rama's worship there before or after crossing to Lanka, and pilgrims bathe in sequence at twenty two wells inside the temple precinct before darshan.
Dwarka in the west is Krishna's city, and the archaeology of submerged structures offshore has attracted both serious survey and a great deal of overclaiming.
The circuit is made by rail, road and air, often across years, and there is no walking version.