Turquoise waters – A letter from Gladys

Question

Letters from Gladys are geography-themed standalone crosswords. Each puzzle has five thematic answers, which are places, sights or landmarks in or around a certain location (in this case, a peninsula). Each thematic answer is notable enough to have its own article in the English Wikipedia, although not necessarily under the same name that is used here. The goal is to fill the grid, identify the thematic answers and guess the name of Gladys’s destination, which is not indicated in the grid.

Dear Puzzling,

The place I am visiting today offers a rich history and an astounding amount of natural beauty. I have relaxed at the beach, dived in turquoise waters and trekked deep into the rainforest to see the remains of an ancient civilisation. Can you guess where I am?

Wish you were here!
Love, Gladys.

Across
1. Places for boring exercise in golf, as well as political promises (8,9)
10. Ned enraged with lack of flamenco in Andalusia, say (4,5)
11. Astronaut identified cutting-edge equipment (7)
12. Staying outside as he was shunned for his crime, kidnapping Mike Pence with force (7)
14. Registration of membership for ten (or, for a change, about fifty) people (9)
15. Bolivian people's magic sauce (4)
16. Taking part in Christian extremist's following (4)
18. Humble doctor cured disease at last (6)
22. Principles from Burgundy: The anchorman retorted vacuous messages (5)
23. Retrospective comic performance about the essence of magical talismans (5)
24. Playing uno in cooperation (5)
25. Prestigious stone thrown in great lake once (6)
26. In Burgundy, the news agency that publishes widely used stylebook shows sudden progress (4)
27. Groundbreaking device appearing after the ending of Das Boot? (4)
30. Suffering isn't fun – drinking energy drinks ultimately leads to poor health (9)
33. Gladys is trapped in Queens, swinging Colts? (7)
34. A role played by Mr Pacino – he got many of his coworkers in trouble for fixing copiers (7)
35. Doctor No given licence to be shown before the initial parts of Tosca, an opera by an Italian composer (9)
37. Surprisingly, he rises so large car can provide transport without the use of 33 across (9,8)

Down
1. "The work of vandals backfired" – Agency's leading agent, Bond (10)
2. Faith reform sure to be stopped by judge on vacation to tropical destination (4,7)
3. Beethoven's work in craft guild (6)
4. Woman perhaps wanting halo? (3)
5. Disturb First Lady with some music in lift (5)
6. Heard from Aquaman: "Greek sea perturbed, with icy island" (9,4)
7. Maybe Dom Pérignon, having been shown the exit, lost all excitement (7,3)
8. Riveter excited soirée endlessly (5)
9. Part of Johannesburg is very rainy? No (6)
13. They say grill exploded entirely? That leads to deep depression (5,4,4)
17. Damaged tail end of truck inside site of ancient city (5)
19. Czech-Haitian criminal skirted law, essentially leading to ruin (7,4)
20. Secretary is wildly erotic, grabbing bottom in spontaneous passion (10)
21. Emphasise anything from 19 down? (10)
28. One was started in a Munich beer hall placed atop school (6)
29. He plays an instrument that's blue, mixed with red and containing a little bit of green (6)
31. Excitement for expensive coat with gold colour (5)
32. Sister devastated, having lost first of two fathers (5)
36. State supporting Oakland's housing (3)

Answer 1

Grid, with thematic answers turquoise:

Explanations:

Across

1. DRILLING PLATFORMS DRILLING + PLATFORMS Places for boring exercise in golf, as well as political promises (8,9)
10. FOLK DANCE (NED + LACK OF)* Ned enraged with lack of flamenco in Andalusia, say (4,5)
11. BUZZSAW BUZZ + SAW Astronaut identified cutting-edge equipment (7)
12. CAMPING CAIN kidnapping MP with G Staying outside as he was shunned for his crime, kidnapping Mike Pence with force (7)
14. ENROLMENT (TEN OR)* about L MEN Registration of membership for ten (or, for a change, about fifty) people (9)
15. MOJO triple def Bolivian people's magic sauce (4)
16. NEXT substring Taking part in Christian extremist's following (4)
18. REDUCE CURED* + (diseas)E Humble doctor cured disease at last (6)
22. NORMS RON< + M(-essage)S Principles from Burgundy: The anchorman retorted vacuous messages (5)
23. TIKIS SKIT< about (-mag)I(-cal) Retrospective comic performance about the essence of magical talismans (5)
24. UNION UNO IN Playing uno in cooperation (5)
25. ASTRAL ST in ARAL Prestigious stone thrown in great lake once (6)
26. LEAP LE + AP In Burgundy, the news agency that publishes widely used stylebook shows sudden progress (4)
27. SHOE HOE appearing after (-da)S Groundbreaking device appearing after the ending of Das Boot? (4)
30. UNFITNESS (ISNT FUN)* drinking E (-drink)S Suffering isn't fun – drinking energy drinks ultimately leads to poor health (9)
33. EQUINES I in QUEENS* Gladys is trapped in Queens, swinging Colts? (7)
34. SERPICO COPIERS* A role played by Mr Pacino – he got many of his coworkers in trouble for fixing copiers (7)
35. RIGOLETTO RIG O LET TO(-sca) Doctor No given licence to be shown before the initial parts of Tosca, an opera by an Italian composer (9)
37. HORSELESS CARRIAGE (HE RISES SO LARGE CAR)* Surprisingly, he rises so large car can provide transport without the use of 33 across (9,8)

Down

1. DEFACEMENT FED< + A + CEMENT "The work of vandals backfired" – Agency's leading agent, Bond (10)
2. ISLA MUJERES ISLAM SURE* containing J(-udg)E Faith reform sure to be stopped by judge on vacation to tropical destination (4,7)
3. LUDWIG W in GUILD* Beethoven's work in craft guild (6)
4. NUN NOUN minus O &lit Woman perhaps wanting halo? (3)
5. PEEVE (EVE EP)< Disturb First Lady with some music in lift (5)
6. AMBERGRIS CAYE AMBER + (GR SEA ICY)* Heard from Aquaman: "Greek sea perturbed, with icy island" (9,4)
7. FIZZLED OUT FIZZ + LED OUT Maybe Dom Pérignon, having been shown the exit, lost all excitement (7,3)
8. ROSIE SOIRE(-e)* Riveter excited soirée endlessly (5)
9. SOWETO SO WET + O Part of Johannesburg is very rainy? No (6)
13. GREAT BLUE HOLE GRATE BLEW WHOLE They say grill exploded entirely? That leads to deep depression (5,4,4)
17. TIKAL TAIL* with (-truc)K inside Damaged tail end of truck inside site of ancient city (5)
19. CHICHEN ITZA (CZECH-HAITIAN)* minus (-l)A(-w) Czech-Haitian criminal skirted law, essentially leading to ruin (7,4)
20. ESCRITOIRE EROTIC* containing S, plus IRE Secretary is wildly erotic, grabbing bottom in spontaneous passion (10)
21. UNDERSCORE ddef Emphasise anything from 19 down? (10)
28. PUTSCH PUT + SCH One was started in a Munich beer hall placed atop school (6)
29. BUGLER (BLUE* + R) containing G He plays an instrument that's blue, mixed with red and containing a little bit of green (6)
31. FUROR FUR + OR Excitement for expensive coat with gold colour (5)
32. SIRES (SISTER - T(-wo))* Sister devastated, having lost first of two fathers (5)
36. GOA substring State supporting Oakland's housing (3)

Credit where due: I had the correct answer for 4d but no idea of the wordplay; samm82 figured it out. (See comments.) Thanks to Jafe for confirming!