Please refer these links.
http://nauyana.org/
http://www.sadahamarana.org/?page_id=48
You can google for these links.
Please do some background checks, before you go there.
False teachers can be exists like infamous 'Pitiduwe Siri Damma'.
buddhism.stackexchange.com/users/6923/John Fonseka
I've heard Mithrigala Nissarana Vanaya is a good place.
I don't know if they do long retreats but most monasteries will accommodate the sincere aspirants.
In Burma, I've personally hoped to someday spend a long retreat at Panditarama (Vipassana) and/or Pa Auk (Samatha).
In Thailand I've considered Wat Chom Tong near Chiang Mai.
There's also the Panditarama center in Nepal .
The Goenka centers are located around the world, as well as in the above countries, but they are aplenty in India, including at Bodh Gaya .
They do 45-60 day retreats, but one needs to work up to it over a few years since they require one to have graduated several preparatory retreats.
The above are all Theravada retreats.
If one is interested in the Mahayana tradition I would unhesitatingly recommend Plum Village in France.
buddhism.stackexchange.com/users/715/Buddho
Rathmalkanda Meditation Center Meditation Techniques Vipassana(Mahasi Sayadaw) Samatha(Anapanasati/ Kasina)
I stayed there for a short period about 8 years ago.
You have to call the number in the website and book in advance.
Mostly foreigners come to meditate there.
Its free of charge but donations are accepted.
Interactions with the locals are minimal.
So you wouldn't face any cultural difficulties.
The food is quite good.
It is situated at a cold mountain area.
So you neither need A/C nor have to worry about mosquitoes and snakes.
Rooms are clean, spacious and have electricity.
The beds are comfortable with warm blankets.
There are several mats lying on the floor as well.
The bathrooms are western style with hot showers.
Attire : Anything that is decent.
It doesn't have to be white.
Rules : Keep quiet and keep clean.
Sila :
Eight Precepts (you will be given refreshments in the evening.
You can bring a snack to eat at nights if you find it hard to keep to the 6th precept)
Usually I got meditation instructions after the breakfast or lunch.
In the evening you can meet venerable Madawala Upali(the head monk) to have a Dhamma discussion.
He speaks English well.
If you are into Abhidhamma or a fan of modern science, you will enjoy the talks as he was a former science teacher and a visiting lecturer of Buddhist philosophy at the Kelaniya University Course duration : 2 weeks.
But you can stay longer or leave before.
buddhism.stackexchange.com/users/111/Sankha Kulathantille
Sri Lanka, Thailand and Burma are the main three Theravada Countries.
In Sri Lanka: Venerable Katukurunde Nananada Thero's Monastery ( http://www.seeingthroughthenet.net ), Mitirigala Nissarana Vanaya (Burmese Panditarama tradition) are for serious practitioners.
buddhism.stackexchange.com/users/11115/A Sri Lankan Yogi
Mitirigala Nissarana Vanaya Teacher-
Ven.
Udairiyagama Dhammajiva Maha Thero (U DhammajivaSayadaw), Excellent knowledge in Dhamma, Pali, Burmese and English, Specialty in Mindfulness and emphasizes the value of mindfulness Meditation Technique - Satipatthana meditation, Burmese Mahasi/Panditarama Technique (Vipassana) and SriLankan Nanarama Method (Vipassana with Samatha) Retreats - 3 days, 7 days, 10 days, 20 days and extensive periods areallowed for serious practitioners and for the meditators who areexpecting the ordaination Location - Mitirigala,Kirindivela, Sri Lanka More Information - nissarana.lk (Official Website) Sanghopasthana Suva Sevana Teacher-
Ven.
Katukurunde Nyanananda Maha Thero (Bhikkhu Nanananda)[A famous book author and a meditation master], Excellent knowledge in Dhamma, Pali and English, Advises not to be in a hurry but to practice Samatha also for aiding Vipassana, Slowly-Mindfully-Carefully.
Appreciates dedication for practicing.
Meditation Technique - Both Samatha and Vipassana, Metta Meditationand probably Sri Lankan Nanarama Method (Vipassana with Samatha) Retreats -
Any time is possible with prior notice.
No allocated dates.
special consideration for dedicated meditators and dedicated practitioners who are expecting the ordaination.
Location - Kirillawala Watta, Dammulla, Karandana, Sri Lanka
More Information - http://www.seeingthroughthenet.net
(OfficialWebsite)
These are two prominent places in Sri Lanka.
Sri Lanka offers 1 year residence visa easily if you have a recommendation beforehand.
Normally in Sri Lanka, temporary ordination is discouraged but permanent ordination is possible at anytime.
Additionally there are more meditation centers which are famous in different aspects.
NaUyana Aranya in Melsiripura (Burmese Pa-auk system), Kanduboda M.C. (Burmese Mahasi System),
Goenka centers in Kandy, Anuradhapura and Kosgama (Burmese Sayagi U Ba Kin system)
buddhism.stackexchange.com/users/12051/user12051
Could anyone provide links and/or info about Buddhist monasteries in Sri Lanka that offer extended meditation retreats?  For those who have taken part in such retreats, how was the experience? Would it be challenging in any way for me, an American, who has never been to Asia before, to travel there/adapt to the culture?  Thank you
Any recommended monasteries in Sri Lanka that offer extended meditation retreats?
buddhism.stackexchange.com
<theravada><monastery>
buddhism.stackexchange.com/questions/11852
buddhism.stackexchange.com/users/4748/Ian
A number of monasteries are recommended in Sri Lanka for a retreat. Moreover, retreats are also possible in Thailand, Nepal and Burma. More information is available on  http://nauyana.org/  and http://www.seeingthroughthenet.net. Moreover, there is a Buddhist monastery in France, Plum Village. Recommended  venues include: Mithrigala Nissarana Vanaya; the  Panditarama center in Nepal; Goenka centers all around the world as well as in the above countries, but they are aplenty in India, including at  Bodh Gaya; Plum Village  in France for the Mahayana tradition; Rathmalkanda Meditation Center - Vipassana(Mahasi Sayadaw),  Samatha(Anapanasati/ Kasina); NaUyana Aranya in Melsiripura (Burmese Pa-auk system), Kanduboda M.C. (Burmese Mahasi System); Goenka centers in Kandy, Anuradhapura and Kosgama (Burmese Sayagi U Ba Kin system). In Sri Lanka: Venerable Katukurunde Nananada Thero's Monastery http://www.seeingthroughthenet.net ), and Mitirigala Nissarana Vanaya (Burmese Panditarama tradition) are for serious practitioners. Sri Lanka, Thailand and Burma are the main three Theravada Countries. A 1 year residence visa is easily available in Sri Lanka if you have a recommendation beforehand. Normally in Sri Lanka, temporary ordination is discouraged but permanent ordination is possible at any time. Suggested links include:  http://nauyana.org; http://www.sadahamarana.org/?page_id=48 ; http://www.seeingthroughthenet.net 
Suggested links include:  http://nauyana.org; http://www.sadahamarana.org/?page_id=48 ; http://www.seeingthroughthenet.net  Recommended  venues include: Mithrigala Nissarana Vanaya; the  Panditarama center in Nepal; Goenka centers all around the world as well as in the above countries, but they are aplenty in India, including at  Bodh Gaya; Plum Village  in France for the Mahayana tradition; Rathmalkanda Meditation Center - Vipassana(Mahasi Sayadaw),  Samatha(Anapanasati/ Kasina); NaUyana Aranya in Melsiripura (Burmese Pa-auk system), Kanduboda M.C. (Burmese Mahasi System); Goenka centers in Kandy, Anuradhapura and Kosgama (Burmese Sayagi U Ba Kin system). In Sri Lanka: Venerable Katukurunde Nananada Thero's Monastery http://www.seeingthroughthenet.net ), and Mitirigala Nissarana Vanaya (Burmese Panditarama tradition) are for serious practitioners. Sri Lanka, Thailand and Burma are the main three Theravada Countries. A 1 year residence visa is easily available in Sri Lanka if you have a recommendation beforehand. Normally in Sri Lanka, temporary ordination is discouraged but permanent ordination is possible at any time. 