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Attached the Map of Sri Lanka for your reference.
Few Places of Interest / National Parks closer and around "Rithika's Hideout":
1) Sigiriya Rock Fortress - was an interregnum of great excitement. Built by Kasyapa who killed his father to gain his wealth, this literal fortress in the sky, is a masterpiece of construction, artistry and irrigation. It was a resort of pleasure, a citadel of beauty and fortress of strength.
2) Dambulla - Dambulla or the Golden Rock is a cave temple, which dates back to the 1st Century BC. Its rock
Ceiling is one large sweep of colourful frescoes, which depict Buddhist mythology, and the tales
Of the Buddha’s previous births. Within the cave temple is the collection of the largest number of Buddha statues in one place.
3) Popham Arboretum - is another interesting excursion for those interested in gaining insight into the trees and foliage of the dry zone. Located about 15 km from Sigiriya along the Kandalama road, this is one of the few arboretums in the country where more than 68 different species of dry zone trees can be identified.
4) Jathika Namal Uyana - is at its best in spring when the Na trees spanning 260 acres burst into full bloom and the earth is covered with a carpet of white petals. On a full moonlit night the white, rose and mauve hues of the seven Rose quarts mountain ranges and their peaks glisten with an ethereal pearly sheen adding an aura of tranquil beauty to the already peaceful atmosphere, wind blown with the soft fragrance of thousands of Na flowers.
5) Anuradhapura - which is the First capital of Singhalese kingdom. At Anuradhapura the extensive ruins spread out from its massive sacred Bo tree, including dagobas, ponds and palaces.
6) Mihintale - Poson, the Full-moon festival commemorates the advent of Buddhism to Sri Lanka in the 3rd Century B.C. The Centre of celebrations is Mihintale (about 10 km From Anuradhapura) where the Buddhist doctrine was first preached by Arahat Mahinda, son of the great Emperor Asoka of India.
7) Ritigala -Mist-shrouded, this 2,514 feet high range was for centuries, a fortress for kings and a retreat for monks.
8) Polonnaruwa - Sri Lanka’s medieval capital between the 11th and 13th centuries. Enclosed within three concentric walls, the city contained royal palaces, bathing ponds, monasteries and
Sacred architecture such as dagobas and image houses.
9) Medirigiriya - This site situated in a beautiful surrounding has a history going in to the pre-Christian times. The brami characters found on the bricks and the some of the stone carvings is an indication of the long history of this site. The first reference to this site in the chronicles is during the king Kanittha Tissa (192-194) of the Anuradhapura Era. Later many kings have contributed to this complex and finally after the invasion of Maga this site too was abandoned when the Sinhalese migrated to the southern parts unable to withstand the torture.
10) Somawathiya & Flood Plains - The Somawathi Chaithya is located by the bank of the Mahaveli River within the Sanctuary named after it and nearly 20 km north east of Polonnaruwa. The flood plains of Mahaveli River have been inhibited by a large number of wild animals ranging from elephants, wild buffalo, deer and other grass-eating animals fed by the luxuriously growing grasslands. The animals are protected by the declaration of Wasgomuwa Strict Natural Reserve, Flood Plains National Park, Trikonamadu Natural Reserve and the Somawathi Chaithya Sanctuary all located to embrace low laying banks of the mighty river.
11) Minneriya National Park - in Sri Lanka there is no better place to watch elephants in the wild than Minneriya National Park, consists of mixed evergreen forest and scrub areas and is home to favourites such as sambar deer, leopards and elephants. However the central feature of the park is the ancient Minneriya Tank (built in 3 rd century AD by King Mahasena). During the dry season (June to September), this tank is an incredible place to observe the elephants who come to bathe and graze, as well as the huge flocks of birds (cormorants and painted storks to name but a few) that come to fish in the shallow waters.
12) Kaudulla National Park - is the latest (actually number 15) to be opened in Sri Lanka. This 6,656 hectare park, which opened in 2002, is an elephant corridor which offers visitors the opportunity to get within close range of the animals. At Kaudulla, near Habarana in the ancient cities zone, it is possible to hire a catamaran to sail on the tank and look out for the elephants, leopards, fishing cats, sambar deer and the endangered rusty spotted cat. August to December is the best time to go.
13) Giritale - is a work in progress. Land by its lake was identified as a tourist resort area more than 30 years ago.
14) Wilpattu National Park - (Willu-pattu) Land of Lakes - is a park located on the island of Sri Lanka. The unique feature of this park is the existence of “Willus” (Natural lakes) - Natural, sand-rimmed water basins or depressions that fill with rainwater. Located in the Northwest coast lowland dry zone of Sri Lanka. The park is located 30km west Anuradhapura and located 26 km north of Puttalam (approximately 180 km north of Colombo). The park is 131, 693 hectares and ranges from 0 to 152 meters above sea level. Nearly sixty lakes (Willu) and tanks are found spread throughout Wilpattu. Wilpattu is one of the largest and oldest National Parks in Sri Lanka. Wilpattu is among the top national parks world renowned for its Leopard (Panthera pardus kotiya) population. The Leopard population in Wilpattu is still not yet known.
15) Wasgomuwa National Park - was originally declared as strict nature reserve in 1938 and then change to a national park in 1984. The park lies within central and north- central provinces. The total park area is 39,322 ha. Park consists of riverine forest, dry mixed evergreen forest, grasslands and wetlands. As park is almost surrounded by Mahaweli & Amban Rivers, riverine forest area is fairly large.
16) Trincomalee - has a strange magnetic charm to it. Maybe, it’s the calmness that gives the place the character of a deep, still pool. Maybe, it’s the azure sea, the pristine beaches, the mysterious Shiva shrine, or the rocks, relentlessly bathed by the rushing waves. Or perhaps it is the town’s fresh, raw beauty.
17) Nilaveli - idyllic palm-fringed beaches lure the sun-seekers continuously, but it’s the sightseeing attractions in the harbour town of Trincomalee close by that keeps them lingering a little longer, namely the Koneswaran Temple, Hot Springs, Swami Rock and Fort Frederick.
18) Matale - Spice Gardens gives you a first hand introduction to the trees, plants and creepers that produces the special spices of Sri Lanka.
19) Kandy - known as The Hill Capital of Sri Lanka, is the home to the stately Temple of the Tooth Relic of Lord Buddha.
20) Royal Botanical Gardens - which began as a pleasure garden for the kings of Kandy, the rich flora of the tropical is exhibited at its best here.