There are many different locations referenced in the epics which you can research at Wikipedia, such as the Himalaya mountains (especially Mount Kailasa) and the Ganges river. You could visit Rama's birthplace in Ayodhya, and then travel far to the south to the location of the Rama Setu, the bridge from India to Sri Lanka. You could then go to the country of Sri Lanka where Ravana once ruled, or perhaps you want to travel to Sita's birthplace, Janakpur, in Nepal. You could visit the hills of Badami, once inhabited by the demon brothers Vatapi and Ilwala, or you could go to the Jatayu Para in Kerala, where Jatayu supposedly fell to the ground after battling Ravana.
For an overview of the many temples and other sacred places of India, see this list at Wikipedia: Hindu pilgrimage sites.
The image below shows the Ram Janaki Birla temple which is located near the main bus station in Ayodhya: