Visiting Kyōto last month, it didn’t take long before I heard one of the more commonly known regionalisms: okini. The singsong way the people of Kyōto say, "Thank you", made me wonder if there were other ways in Japan of expressing one’s gratitude. I was surprised by what I discovered. I have put together a list of some of these local sayings.
Incidentally, the original meaning of arigatō (有り難う) conveyed the sense that the thing you were thanking a person for something that had been difficult for them to do (有るものが難しい) and you felt bad for having them do it. Dōmo (どうも) comes from dōshite-mo (どうしても), and emphasizes the feeling of gratitude or regret.
 This is still a work in project and I will try to clean this up in the coming days. 
Hokkaidō
1. Hokkaidō
Hokkaidō-ben
  どうも!
    Dōmo!
(Common among friends.)
  どうもね!
    Dōmo-ne!
(Same as saying dōmo.)
有り難う
  Arigatō!
(Standard Japanese.)
なんも、なんも
  Nanmo, nanmo!
(Includes the feeling of sorry, don’t worry about it.)
 
Tōhoku 
2. Aomori
Tsugaru-ben
  ありがどごしてす
    Arigado goshidesu!
(This is the polite form.)
  めやぐだの~
    Meyagudanoh!
(Similar to saying meiwaku-o kakemashite sumimasen, sorry for causing you trouble.)
  どうも
    Dōmo!
(Same as Aomori.)
3. Iwate
4. Miyage
5. Akita
ぶじょほーだんし
  Bujohohdanshi!
(Originates from the word buchōhō, meaning carelessness or blunder, sorry about that.)
どんも、おぎぃなぁ
  Donmo, ogi-nā!
おぎぃ
  Ogi!
(Southern Akita prefecture, i is shortened with falling accent.)
6. Yamagata
Yonezawa-ben
  おしょうしな
    Oshōshina!
(Not commonly used among youths.)
Shōnai-ben (northwestern Yamagata)
  もっけだ
    Mokkeda!
(Can be used to mean arigatō, gomen, dōmo, and so on.)
7. Fukushima
 
Kantō
8. Ibaraki
Ibaragi-ben
  どーもね
    Dōmo-ne!
9. Tochigi
 すいません
  Suimasen!
(Used when receiving something.)
10. Gunma
11. Saitama
Chichibu Region
  わりぃねぇー
    Warine~!
(Saying warui-ne but including the feeling of gratitude.)
12. Chiba
13. Tōkyō
Arigatō!
14. Kanagawa
 
Chūbu
15. Niigata
いかったいね
  Ikattaine!
あんがとの
  Angatono!
(Means arigatō-ne.)
おーぎにはや
  Ōginihaya!
(North-central Niigata prefecture. Nearly extinct saying.)
いやいやいやいや、ど~もっス
  Iya iya iya iya, dōmossu!
    (May be a personal tick.)
16. Toyama
 あんがとう
  Angatō!
  (Seems to be falling into disuse.)
Toyama-ben
  気の毒な
    Kinodoku-na!
(Expresses regret at having troubled someone by doing something for you.)
  だいてやっちゃ
    Daiteyaccha!
(Used when someone treats you to dinner or drinks.)
17. Ishikawa
Kanazawa-ben
  あんやとごぜえみす
    Anyato gozēmisu!
  あんやと
    Anyato!
18. Fukui
19. Yamanashi
20. Nagano
Shinshū-ben
  あいとうですぁ
    Aitō desu-a!
(Intonation similar to Kansai dialect. Desu-a is a contraction of Desu-wa.)
Īda-ben
かんな
    Kanna!
(Kaniya is also said.)
  おかたしけ
    Okatashike!
(May be a corruption of katajikenai, which means to be grateful.)
  おしょーしー
    Oshōshī!
(Second and third syllables are extended. Includes the feeling of obligation and gratefulness.)
  うれしいに
    Ureshi-ni!
(Means one is happy/delighted, but conveys the same meaning as arigatô.)
  ありがとや
    Arigatoya!
(Arigato-na! is also possible.)
21. Gifu
22. Shizuoka
Enshū-ben
  ありがとね
    Arigato-ne.
23. Aichi
Nagoya-ben
  ありがと
    Arigáto!
(Accent on the ga, shortened to.)
  ありがとさん
    Arigato-san!
(A casual way to say thanks.)
 
Kansai
Ōkini!
Maido ōkini!
24. Mie
 おおきにいー
  Ōkinī!
   (Accent on the final syllable.)
25. Shiga
26. Kyōto
  おおきに
   Ōkini!
(More common among the elderly. Intonation is important.)
27. Ōsaka
 おおきに
   Ōkini!
 ありがとー
  Arigatoh!
(Intonation is key, rising on last syllable.)
 ありがとさん
   Arigato-san!
まいどおおきに
  Maido Ōkini!
(Used when, for example, thanking someone for their continued patronage.)
28. Hyōgo
 Yura-ben (Awaji-shima)
   おおきによ
    Ōkiniyo!
 
29. Nara
30. Wakayama
 
Chūgoku
31. Tottori
 Yonago-ben
  だんだん
    Dandan!
(Not common with younger residents of Yonago City.)
 ようこそ
  Yōkoso!
(In standard Japanese this phrase is said when expressing the gratitude felt when someone visits you.)
32. Shimane
33. Okayama
 ごめんよぉ
  Gomenyō!
   (Used by women. Accent on go.)
 わりいなぁ
  Wariinā!
すまんなぁ
  Sumannā!
(These two are used by men.)
34. Hiroshima
 ありがとね
   Arigato-ne!
(Accent placed on the ga and ne.)
 すまんのう
  Sumannō!
(Similar to sumimasen in meaning. More common among the elderly.)
35. Yamaguchi
  ありがとうあります
   Arigatō arimasu!
すまんのう
  Sumannō!
    (Meaning is closer to arigatō (thanks) than sumimasen (sorry).)
Iwaguni
  すまだったねー
   Sumadatta-nē!
    (Strong accent on the final nê.)
 
Shikoku
36. Tokushima
Awa-ben (Northern central Tokushima prefecture.)
  あんとー
    Antō!
(May be nothing more than baby talk.)
  おおけに
    Ōkeni!
  ありがとぐわした
    Arigato guwashita!
37. Kagawa
ど~~も
  Do~hmo.
(Be sure to let the word fall languidly from your lips.)
38. Ehime
39. Kōchi
 
Kyūshū
40. Fukuoka
 ありがとー
  Arigatō!
(Intonation and accent, like many of these is key. Spoken in a quick staccato, with an accent on the end.)
 だんだん
  Dandan!
    (Apparently, this saying is fairly common among elderly women, but in all my years living in Fukuoka, I’ve never heard it. Means thanks so much.)
41. Saga
すんまっせん
  Sunmassen
あんがとー
  Angatō!
あんがちょー
  Angachō!
おおきに
  Ōkini!
(Same as Kyōto. Another person from Saga told me that no one says this.)
42. Nagasaki
 Iki-ben (Islands in Nagasaki prefecture, west of Fukuoka prefecture.)
  おおきん
    Ōkin!
(Similar to ōkini.)
43. Kumamoto
 すんまっせん
  Sunmassen
    (Also means excuse me, as in sumimasen.)
しょうじょう
  Shōjō!
   (An elegant way of saying thanks.)
44. Ōita
45. Miyazaki
 あいがと
  Arigato!
   (Said with rising inflection.)
46. Kagoshima
  あいがとごわした
   Aigato gowashita!
おおきに
  Ōkini
  (Common among those born before 1955.)
あいがとさげもした
  Aigato sagemoshita!
   (Original Satsuma-ben. A polite expression)
あいがともしゃげもした
  Aigato moshagemoshita!
    (Polite form.)
Amami Ōshima (a collection of islands halfway between Kyūshū and Okinawa)
  ありがっさまありょうた
    Arigassama aryōta!
 
Okinawa
47. Okinawa
 にへーでーびる
   Nihēdēbiru!
Miyako-jima-ben
  タンディガータンディ
    Tandigātandi!