It really depends on how the board falls. You could make a legit case for multiple teams...so let's do it:
NYG (my favorite trade back scenario)
Why the Colts would do it: Because the NYG's 2nd round pick would certainly be in play. It might require sending back one of the later 4th round picks...but it would be worth it. There are going to be a lot of good players available in the 2nd round...so having two cracks at them would be huge. Also, while the Colts would be sacrificing 8 spots in the 1st round...many of those spots will likely be offensive players...so the Colts will still be able to get a guy they like on defense.
Why the NYG would do it: Beyond an aging Eli, the NYG are built to win now. After going on a FA spending spree, they have built an elite defense. But the offense is not quite up to that level. They signed Marshall to compliment OBJ and Shepard...but they are still lacking that dynamic threat at TE or RB. So a playmaking RB or TE could be seen as the final piece to a Super Bowl team. Or they could be looking to solidify their OL with a top prospect who they can plug in day one. Either way, a team in their position is much more likely to be willing to sacrifice a 2nd round pick to win now.
Targets: McCaffrey, Howard, Njoku, Cook, Ramczyk
Why the Colts would do it: Because the Colts would only be moving back five spots...and would gain at least a 3rd round pick to increase flexibility in rounds 2-4. Of those five spots, only WAS appears to be a threat to the players the Colts are targeting.
Why DEN would do it: Like the NYG, DEN has an elite defense...but is in need of TE like Howard or Njoku. However, their most glaring need is OL. They could just let it play out and take whichever OL player falls to them. But to ensure that they get their guy, they could move up five spots in front of BAL. DEN also has a 3rd round comp pick, which would make it much easier to accept losing a 3rd round pick.
Targets: Howard, Ramzyck, Bolles, Robinson
Why the Colts would do it: For the same reasons as they would trade with DEN.
Why TB would do it: TB signed DJax in FA, but they are still looking to build up the weapons around Winston. So they could be targeting a RB, TE or even a WR. In order to get their guy or even the top remaining guy, they will have to at least get in front of TEN. And even then WAS and BAL could be a threat. So it would be best to just move up and take their guy at #15.
Targets: Howard, McCaffrey, Cook, Williams, Davis
Why the Colts would do it: Not sure they would, but Ballard did trade with NE...so he might not be averse to trading with rivals. And the Colts would only be moving back a few spots and taking away a pick from that rival.
Why TEN would do it: Not sure if they would. But if TEN drafts one of the top secondary players with their first pick (which they should do), they will be looking to get one of the top WRs at #18. Likewise, they could be looking to target Howard to replace Walker. Regardless, at WR, there's a good chance that only one will still be available at the Colts pick. BAL and WAS would both be threats to take that player. So to ensure that they get their WR, TEN would want to jump in front of them...as they don't pick again until #83, at which point even the second tier WRs will be gone. But even if two WRs are available, they still might have a preference. Also, like DEN, they have a 3rd comp pick, which makes it easier to trade their 3rd round pick.
Targets: Howard, Davis, Williams, Ross
Beyond that, you could make a case for DET and OAK...or most teams. Howard is a common theme for trade back scenarios, as I think several teams would be calling the Colts if he is still there. But even if Howard isn't there, there are scenarios that put the Colts in the driver's seat. The ones I listed are just the most likely, IMO. I wouldn't put it past Ballard to trade all the way to the bottom of the 1st round, if the deal is good. Regardless, I think he will have a nice little bidding war for #15 if the draft falls favorably for it.