Sea turtles are amazing creatures, and I would like to share some locations where you can meet them close up. Luckily there is still quite a few places on earth where you can see them, but maybe not for long.
Australia has several places where you can see mostly Green Sea Turtles (Chelonia mydas) but also you may be lucky an encounter flatbacks (Natator depressus) which you find only in Australia and Papua New Guinea. Also Leatherbacks (Dermochelys coriacea) and Loggerheads (Caretta caretta) swim in Australia waters. I recommend Ningaloo reef area on the west coast and Heron Island which is located in the very south of Barrier Reef on the east.
Costa-Rica is a country where you can see sea turtles around the year. Spring and summer time on Caribbean side (Tortuguero, Cahuita) and fall/winter time on the Pacific side. In Costa-Rica you may find 4 different species of sea turtles. Especially interesting is to see arribada of the Olive Ridleys (Lepidochelys olivacea), in Ostional National Wildlife Refuge. Other Central-American countries also have locations to see sea turtles.
Caribbean islands have also excellent places to see Sea Turtles. I have just snorkelled with Green Turtles in Tobago Cays and I work in Carriacou Island in Grenada in a sea turtle conservation project. On the beach I get close to Hawksbills (Eretmochelys imbricata) and Leatherbacks. Other Islands also have places where you can see these species.
Kemp's Ridleys (Lepidochelys kempii) you can see mainly around Gulf of Mexico and they nest in Mexico and sometimes Padre Island in Texas. I have not yet been there, so can not recommend any specific location. Kemp's Ridleys also do arribada's where hundreds, maybe thousands of turtles come to nest at the same time.
In Europe you can see Loggerheads for example in southern Italy, Greek islands of Zakyntos, Kefalonia, Crete and the Peloponese as well as in Turkey.
Besides these mentioned here, there are several other locations where you can see them. To get real close to these creatures and learn more, I recommend joining as a volunteer in one of the conservation projects around the world. I have done several myself. More about volunteer projects http://www.ekomatkaajat.fi/