Here is the world map. It should go without saying that it contains massive spoilers.
This map was taken from the following wiki: https://sites.google.com/site/yamabikoriji/batorikusu-gong-e. It's missing the path that leads to the Shadow Smith and the Drift Ice area.
Most squares should be obvious. The only exception are the red colored squares, which are squares that require you to find and destroy secret statues before they appear.
Locations of caves containing diamond shards are not shown on the map and can be found on the diamonds page.
1. Sundale Castle
2. Sundale Village
3. Spendthrift Smith
4. Continental Tunnel (LV ?)
5. Wellwends Village
6. Thorswood Village
7. Jumbo Smith
8. Grumlin Lair (LV 8.7)
9. Moonluna Village
10. Dainty Smith
11. Freigold Town
12. Freigold Mines (LV 11.0)
13. Thermal Gas Vents (LV 9.0)
14. Blackened Smith
15. Twoburn Village
16. Whitesmith
17. Dark Cave (LV 11.0)
18. Santurn Town
19. Santurn Grotto (LV 13.6)
20. Ironheart Town
21. Bandit Hideout (LV 18.0)
22. Knightonia
23. Musclebound Smith
24. Niuros Hideout (LV 8.0)
25. Moonluna Cave (LV 6.8)
26. Wherewhither Woods (LV 16.5)
27. Lukewarm Village
28. Snow Cave (LV 22.5)
29. Giant's Den (LV 25.0)
30. Bargain Smith
31. Bear's Den (LV 24.0)
32. Floating Isle Tower
33. Dupet's Fortress (LV 10.0)
34. Uncharted Cave (LV 24.2) * Claiming this square opens new locations on the map *
35. Soaking Smith
36. Amphibizon Village
37. Serpent Swamp (LV 28.9)
38. Smashfist Smith
39. Revolver Village
40. Bobbencreast Coast (LV 25.5)
41. Buldorg's Fortress (LV 24.2)
42. Crab Hollow (LV 7.4)
43. The Synthesizer
44. Raging Smith
45. Uncharted Cave (LV 27.0) * Claiming this square opens new locations on the map *
46. Twilighton
47. Prison Cave (LV 29.0) * Rescue Shocking Smith. Make sure to rescue the Apprentice Smiths from the surrounding caves first, they go away after you rescue the smith. *
48. Shocking Smith
49. Mentalis' Fortress (LV 31.2)
50. Gomogomo Village * Highlighted Path is the easiest way through the mountains *
51. Sealed Cave (LV 34.7) * Claiming this square opens new locations on the map *
52. Sealed Cave (LV 34.7) * Claiming this square opens new locations on the map *
53. Sealed Cave (LV 36.1) * Claiming this square opens new locations on the map *
54. Land of Demons (LV 37.0) * Fight Mentalis Here *
55. Sealed Cave (LV 36.1) * Claiming this square opens new locations on the map *
56. Dark Hall (LV 38.0) * Lord Jhagur's location. Square above unlocks the land of Drift Ice *
57. Path to Shadow Smith
58. Path to Drift Ice