What was the 1st attempt to have a Theravada monastery in the West? Venerable Nyanatiloka had tried to setup a monastery in the West. Were there previous attempts? How successful were they? Do they still exist? If not, what happened? 

Following is the link "Plans for a Theravada Buddhist monastery in Europe" with regard to this exercise. Extract as follows:


  Upon returning to Germany, Markgraf planned to found a Buddhist Monastery in the southern part of Switzerland and formed a group to realise this aim. Enrico Bignani, the publisher of Coenobium: Rivista Internazionale di Liberi Studi from Lugano had found a solitary alpine hut at the foot of Monte Lema Mountain, near the village of Novaggio overlooking Lake Maggiore, and Nyanatiloka left Burma for Novaggio at the end of 1909 or the beginning of 1910. The architect Rutch from Breslau had already designed a monastery with huts for monks, and the plan was that Bhikkhu Sīlācāra and other disciples were to join Nyanatiloka there. Nyanatiloka's stay and plans drew a lot of attention from the press and several journalists visited him to write about the him and the planned monastery. However, Nyanatiloka suffered heavily from bronchitis due to the cold weather, and also from malnutrition, and after half a year left Novaggio with the German monk candidate Ludwig Stolz, who had joined him at Novaggio, to try to find a better place in Italy or North Africa. In Novaggio he worked on his Pāli-grammatik (Pāli Grammar) and his translation of the Abhidhamma text called Puggalapaññatti (Human Types).
According to this timeline, Theravada had the following significant times

http://www.buddhanet.net/e-learning/history/thera_timeline.htm


  1899  • First Western Theravada monk (Gordon Douglas) ordains, in
  Burma.
  
  1958   • Ven. Nyanaponika Thera establishes the Buddhist Publication
  Society in Sri Lanka to publish English-language books on Theravada
  Buddhism. • Sarvodaya Shramadana Movement is founded in Sri Lanka to
  bring Buddhist ideals to bear in solving pressing social problems. •
  Two Germans ordain at the Royal Thai Embassy in London, becoming the
  first to take full Theravada ordination in the West.


The Insight Meditation Society predates the first monastery


  1970's     • Refugees from war in Vietnam, Cambodia, and Laos settle in
  North America, Australia and Europe, establishing many Buddhist
  communities in the West. • Ven. Taungpulu Sayadaw and Dr. Rina Sircar,
  from Burma, establish the Taungpulu Kaba-Aye Monastery in Northern
  California, USA. • Ven. Ajahn Chah establishes Wat Pah Nanachat, a
  forest monastery in Thailand for training Western monks. • Insight
  Meditation Society, a lay meditation center, is founded in
  Massachusetts, USA. • Ven. Ajahn Chah travels to England to establish
  a small community of monks at the Hamsptead Vihara, which later moves
  to Sussex, England, now known as Chithurst Forest Monastery.
  
  1980's     • Lay meditation centers grow in popularity in North America,
  Australia and Europe. • First Theravada forest monastery in the USA
  (Bhavana Society) is established in West Virginia. • Amaravati
  Buddhist Monastery established in England by Ven. Ajahn Sumedho.


Depending on what your thoughts are on The Insight Meditation Society, you may consider that an earlier "monastery" and how strictly you interpret monastery.