In Hinduism, Ramayana and Mahabharata are ‘ithihasas’ (history). So it is only natural to stumble upon places mentioned in the Ramayana. In the modern day Sri Lanka 
After Kidnapping Sita, Ravana took her to Seetakotuwa or Sitakotuwa. The place was then known as Goorulupota. It is believed that Mandodari, the wife of Ravana and the Queen of Lanka lived here. Seetakotuwa is about 10 km from Mahiyangana and ruins of a prosperous city can be found here. 
In the Ramayana, Sita was held captive in the Ashoka Vana (forest) and this place is the present Sita Eliya in Sri   Lanka 
It is believed that Hanuman after finding Mata Sita at the Ashoka Vana, used the Ritigala  Mountain India Sri   Lanka South India . It is also believed that a part of the mountain from the Himalayas  with herb carried by Hanuman fell at Ritigala. A particular area in Ritigala, even today possess vegetation which is remarkably different from the surrounding areas and the area contains many herbs. 
The rest of the mountain brought by Hanuman is found at Rumassala which is situated in the southern coast overlooking the Galle   Harbor 
Other places of interest include, Ravana Kotte in the south eastern coast of Sri Lanka 
Another interesting place is the Ravana Ella cave. It is said that on hearing Lord Ram and his army approaching, Ravana moved Sita deep into the jungle to the place known as Ravana   Ella  Cave 
Sculptures, stone works and granite slabs can be found at Maligawa Tenna near Welimada and it is believed that it was an important place associated with Ravana’s Kingdom. 
It is now believed and advertised that the legendary Pushpaka Vimanam (flying machine of Ravana) could have landed at Werangatota, about 10 km from Mahiyangana, east of Nuwara Eliya. 
Yudhaganapitiya, north of Nuwara Eliya, is believed to be the spot where the Rama-Ravana battle took place. There are boulders scattered here and many have dents from the result of the epic battle.
Apart from this there are numerous other places associated with the epic Ramayana.