It's tough to pick places to do aways, especially if you have no real driving reason to go to a place (ie you're from the area, wife wants to be near family, etc). It's even tougher to find out what "competitive" programs are, because as we all know, ortho is a very competitive field. When I was picking aways, I had one definite in mind, which was closer to home, and then I almost randomly picked the other based on their "reputation" and by eliminating other places that were in areas of the country that I just really didn't want to be in. In the end, the place that I definitely had in mind ended up pretty far down on my rank list, while the random place that I roatated at was at the top of my rank list, and is where I ended up matching.
Like I said, I think all ortho programs are competitive. Just because you do an away doesn't mean that you're in. But, if you don't have a real geographic preference, I would consider doing aways at places that are known to heavliy favor their rotators. Examples would be UTSW and Northwestern where 5/6 or 7/9 of their residents in each class were rotators. There have been previous posts that discuss which porgrams heavily favor their rotators.
My other piece of advice would be to try and do that 3rd year ortho rotation at the very end of 3rd year. Also make sure that they know you want to go into ortho and that this is your ortho sub-i, especially if there are other students doing ortho who have no interest in going into it. Almost all the people who went into ortho from my school did 2 weeks of ortho as a third yeard during our surgery rotation as well as a bunch of other people because they didn't want to do 2 weeks of urology, but then we all did another month as a 4th years, which was what counted as our ortho rotation. So just think about things and also ask people at your school for advice.