First, some background. MLB clubs sign Player Development Contract with minor-league teams to provide facilities for their players to play in. The MLB club controls the on-field personnel (players and coaches), while the minor-league team manages the stadium, the clubhouse, etc.
There are very specific rules governing these PDCs. To protect both the MLB organization and the minor-league organization, there is a very small window of time for affiliation shifts, which is usually the last two weeks of September every two years. PDCs can only be signed or extended for two or four seasons, ending in even-numbered years (2014, 2016, etc) The period between September 16 and 30 essentially is a free agent period for minor-league teams. If an minor-league club has not signed a PDC by the end of the period, MLB will assign a club to an minor-league team, assuming there's an equal number of minor-league and MLB organizations.
Most of the Cleveland's minor-league affiliates are either in Ohio (Columbus, Akron, Lake County, Mahoning Valley) or are in "complex league" (in which the teams play in stadiums owned by the club). The Arizona League and the Dominican Summer League are complex leagues, so there's no chance of shifts with those teams. So Cleveland's minor-league affiliates have been stable since they shifted their AAA affiliation from Buffalo to Columbus in 2009.
The only affiliate that isn't in Ohio or owned by the club is the Carolina Mudcats, the High-A affiliate. The Mudcats were previously known as the Kinston Indians, but in 2012, through a series of purchases and moves, shifted their operations to Zebulon, North Carolina, and took on the name of a Southern League (AA) team that had just moved. But even though the name and location of the club had changed, the Indians have had an affiliation with Kinston/Carolina since 1987, which is one of the longest relationships in professional baseball.
But it looks like that's about to change. The Indians and Mudcats did not renew their PDC, so they both can find new partners.
On September 16th, there were six MLB clubs without High-A minor-league clubs...
Atlanta Braves (2014 team: Lynchburg)
Chicago Cubs (2014 team: Daytona Beach) signed PDC with Myrtle Beach 9-16
Cincinnati Reds (2014 team: Bakersfield)
Cleveland Indians (2014 team: Carolina)
Seattle Mariners (2014 team: High Desert)
Texas Rangers (2014 team: Myrtle Beach)
...and six High-A minor-league clubs without MLB affiliations:
Bakersfield Blaze (California League)
Carolina Mudcats (Carolina League)
Daytona Cubs (Florida State League)
High Desert Mavericks (California League)
Lynchburg Hillcats (Carolina League)
Myrtle Beach Pelicans (Carolina League) signed PDC with Cubs 9-16
Geography can play some part in the decision (close to the fanbase, ease of moving players between clubs), but the minor-league facility and organization is also a factor. For instance, the Indians stayed in Kinston for many years largely because the playing surface there was so good.
The Cubs have since signed a PDC with Myrtle Beach, which means that there are only two open spots remaining in the Carolina League (Carolina and Lynchburg), and three teams in the Eastern Time Zone: the two Carolina League teams plus Daytona. I would assume that the Indians wouldn't want to move their High-A affiliate to the West Coast (it would create travel delays when promotions/demotions are made), so that would seem to leave Lynchburg and Daytona as the two main options. In the linked article, it mentioned that the Daytona owner was in Ohio, which could mean he's talking to either the Indians or Reds, who are both looking for new minor-league teams.
For much more information on the affiliate shuffle, check out this post at Baseball America; it's updated daily as news comes in.