This is not an answer, just an observation.  The probability of returning to the origin eventually
is 1 (approaches 1 as the number of steps approaches infinity).  This is Pólya's famous 1921 [result][1]. The same is true for reaching any fixed point $(x,y)$: the probability of reaching it is 1.
<strike>
My *guess* is that the probability of reaching $(x,y)$ before hitting the origin (or any other fixed point) is likely still 1.  But this is only a guess</strike>. 
As pointed out in the comments, this was a terrible guess!


  [1]: http://mathworld.wolfram.com/PolyasRandomWalkConstants.html