Non-wealthy (English) Chinese University teacher trying to plan a non-expensive Hainan holiday

Well, it's a big province in China, which contains many cities.
You can stay at Sanya. According to your requirements, it's suggested to stay at Tujia Sweetome Vacation Rentals (Sanya Shiji Haoting). It's close to the beach. The price is about CNY 300 per night. It's located at No. 1 Fenghuang Road. There is Dadonghai you can wim in. Or you can take bus to Sanya Bay or Yalong Bay to swim; the quality of water is better. :-)

Than you so much for your help and advice.. any recommended coastal islands with similar qualities to my initial question? I was also wondering if it might be possible to visit the reserve where the rare gibbon is? (the world's rarest and most endangered primate as I understand)

Well, to meet all your demand, you may consider the Qiziwan Beach in Changjiang Li Minority Autonomous Region for quietness and simplication. More importantly, it is close to the Bawang Ridge Natural Reserve, where the rare gibbon are inhabited. Tourists are allowed to visit the reserve, but there are some restricted areas where you cannot enter. As the number of gibbons are very limited, it is hard to know if you have a chance to see them.

Thank you so very much once again for your most knowledgeable and helpful response! :>