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Naturally, there's some disagreement about where these places were exactly. Here are the views I was able to find so far (and I'll add more if I find any other views):
Rabbi Prof. Shmuel Klein in his essay in Hebrew "מחקרים בפרקי היחס בדברי הימים" (Studies in the Genealogy Chapters in Chronicles), Tzion vol. 3, pg. 2, wrote (my translation):
"Korach that is mentioned first is not the name of a clan or a family but the name of a place. Among the warriors of David we find five who were mentioned with the title "the Korachites" (Chronicles 1:12:6-7) all coming from one place, that although was not mentioned anywhere else in Tanach, was mentioned in an ancient mishna from the time of the [Second] Temple as a place that is enriched by its wine. The form of the name there is "Korchaim"1 and its memory is preserved until this day south of the Dead Sea in the name of "Wadi il-Korachi"2 in a very fertile area."
The New Guide to Israel (מדריך ישראל החדש) (edited by Seffi Ben Yosef), pg. 114, on the other hand, identifies Kerotaim with the Samarian Arab village Qarawat Bani Hassan. This is apparently based on Yeshayahu Press's view as brought in his book.
Lastly, according to this post, Dr. Michael Avi-Yonah apparently identified it with Coreae. However, that might be a separate place. See here.
Prof. Aharon Demsky in his essay "Qumran Epigraphy and Mishnaic Geography", Dead Sea Discoveries, 4:2, suggests per archeological finds of inscriptions that say things such as "Yochanan Chatla" (יוחנן חטלא) that Hattulim or Chattulim was perhaps a town or the name of a family that lived in the vicinity of Jericho and Qumran. However, there are those that disagree with his readings of these particular inscriptions, which means that it's also possible that they are not evidence for the location of the town or family.
Rabbi Klein in his book Eretz Yehuda (Land of Judea), pg. 140-141 wrote that he thinks Chattulim was somewhere in the vicinity of Korchaim (or Karuchim, as it's spelled in this book), which would mean that he places it somewhere around Wadi il-Korachi.
1 Per the manuscript variant that Rabbi Klein had before him (probably either MS Kaufmann or MS Parma of the mishna).
2 This is apparently some place near what is currently identified as the Biblical Tzoar.