Bill and Sam choose Summit, Alabama as a location for the kidnapping because, within the time frame of this story, the Appalachian area in northern Alabama is remote and sparsely populated. Sam also considers the people rather backward.

It contained inhabitants of as undeleterious and self-satisfied a class of peasantry as ever clustered around a Maypole.

Furthermore, the two men know that without any large city nearby, the law enforcement in this town must be minimal. 

We knew that Summit couldn’t get after us with anything stronger than constables and, maybe, some lackadaisical bloodhounds and a diatribe or two in the Weekly Farmers’ Budget.

Sam and Bill also assume that they have little to fear about any interference with the success of their plans. Because they stay about two miles away, at an elevated point where there is a cave in which to store their provisions, the men feel that they can safely keep a lookout over the town and spot any unusual activity in time to escape.

Indeed, the humor of this story lies in Bill and Sam's erroneous assumptions about the residents of Summit and their expectation that kidnapping the son of the richest man in town will be easy and profitable to them. For in the ironic reversal of O. Henry's ending, Bill and Sam are the ones who have been terrorized, not the kidnapped boy. Pretending he is Red Chief, the boy tortures his captors both physically and psychologically. Also, the wealthy "mortgage fancier and forecloser" Dorset refuses to pay the ransom, demanding, instead, that they pay him to take his son back.

Why do Bill and Sam choose Summit as the location for the kidnapping in "The Ransom of Red Chief"?

The explanation for why Sam and Bill choose Summit as the location of their kidnapping scheme occurs in the first three paragraphs of the story. Since the story is told in the first-person point of view by Sam, who is an unreliable narrator, readers must take what he says with a grain of salt and read between the lines to get the real meaning. Sam gives a few reasons for choosing Summit and hints at others.

The reasons Sam gives for choosing Summit are that "philoprogenitiveness ... is strong in semi-rural communities" and that the law enforcement and journalism in the town are inept. The concept that philoprogenitiveness, or loving one's offspring, varies by type of community is ludicrous on its face. People in the city and in the country love their children as much as those in "semi-rural communities," so this explanation is more of a fabricated rationale than a well-considered reason. The real reason for choosing Summit seems to be that it was convenient to where they were at the time when they hatched the plan. They needed money to carry out their fraudulent scheme in Illinois, but they only had $600 between them, so they wouldn't want to waste their funds on travel. 

Sam suggests that "other reasons" besides philoprogenitiveness were behind the decision. These seem to be the lack of competent policing and the shortage of hard-hitting journalists in Summit. Sam and Bill thought they could easily escape the "constables" and "lackadaisical bloodhounds" that might come after them. And rather than dispatching "reporters ... in plain clothes" like the city newspapers sent out to "stir up talk about" kidnappings, Summit was only likely to publish "a diatribe or two" in the weekly farm paper. 

In addition to these stated reasons, there is another hint from Sam as to why they chose Summit. They believed the inhabitants of the town were "undeleterious," that is, harmless, and that they were self-satisfied, meaning that they might be so content with themselves that they could be easily deceived. How did Sam and Bill reach this conclusion about the residents of Summit? Perhaps simply because of the fact that they had named their town Summit even though it was "as flat as a flannel-cake." It's possible that Sam and Bill figured that people who would name a flat town "Summit" could be easily manipulated. Unfortunately for Sam and Bill, that decision, made "during a moment of temporary mental apparition," turned out to be a poor choice. They jumped to a conclusion about the people of the town but met their match in Ebenezer Dorset. 

Why do Bill and Sam choose Summit as the location for the kidnapping in "The Ransom of Red Chief"?

Bill and Sam choose Summit as the location of the kidnapping because they feel that "philoprogenitiveness. . . is strong in semi-rural communities." According to Merriam-Webster dictionary, the word "philoprogenitive" refers to either a love for one's offspring or a prolific ability to produce offspring.

Bill and Sam imagine people there probably either love their offspring very much or have enough offspring that one will be easy to kidnap. Bill and Sam eventually settle on the child of a prominent citizen named Ebenezer Dorset; they gamble that Mr. Dorset will be appropriately dismayed enough at the kidnapping of his son to hand over a ransom of two thousand dollars for his release.

Also, Bill and Sam don't have much respect for the abilities of law enforcement officials in Summit. They think the town wouldn't be able to get after them "with anything stronger than constables and, maybe, some lackadaisical bloodhounds and a diatribe or two in the Weekly Farmers' Budget." The small-time crooks believe the police force in Summit is too incompetent and understaffed to prove any sort of a threat to their kidnapping scheme. Since they believe they won't face many repercussions for their actions, Bill and Sam decide to choose Summit for the location of the kidnapping.