The distance to where the big bang theoretically happened would be "0" (and this should be true for any point within the universe). The entire universe was theoretically produced in the big bang, with every point in space being "inside" the big bang. The whole universe is very special, it is amazing what is out there (including black holes, earth, stars, planets, nebulae, etc...).
Whether or not there is even a "center" to the big bang / the universe, however is another related interesting question. Current models seem to indicate that there is no center. It would be interesting if there is a true center of the universe, and would be interesting to know if there is anything special about the center if it exists.
The question of whether or not there is a center of the universe is addressed in the following links:
What is in the center of the universe?