Yes, there are battleground states. I grew up in one of them -- Missouri. And without those states, the middle United States would never see a presidential candidate. Candidates go to big cities for the same reason bank robbers go to banks -- each contain what they want.
We NEED battleground states because of states like California, where about half the precincts voted Republican, but all the big cities (and hence the popular vote) went to the Democratic Party. (An example, if one was needed, of what would happen if there were no electoral college in the nation).