Tips for getting the wheel back on?

[tzvia]

Owlie-
Are those modern dual pivot brakes (current road bike type?). If so, they may have an adjustment screw. Look for a small allen key screw on the top, usually on the side opposite the cable side. Turning that screw will rock the brakes to one side or the other. If the brakes don't have that fine adjuster, you would need to loosen the back allen key bolt some, move the brake into position, then while pulling the brakes hard, tighten the screw. And yes, it's on the back of the 'brake bridge', that cross bar the brakes are attached to, in the recessed hole. Doing it that way is a fine art as the brake tends to rock out of adjustment as you tighten it. Thankfully my brakes have that little screw on top.

[OakLeaf]

If the brakes were centered before, I'd see if you could coax the caliper a little harder, before readjusting anything.

Here's Shimano's service manual for the R560 brakes, which should be nearly identical to the ones you have. (I <3 Shimano's website.) As tzvia said, fine-tuning with the adjustment screw (step 4 on the manual) is a whole lot less of a pain than re-centering the caliper with the mounting bolt.

[aicabsolut]

If you are having to tug pretty hard to get the tire to clear the brakes, then that is probably why you are knocking them off center.