Steering wiggles

I'll check the steering bolts asap. These are brand new tires (less than 250 miles) and it has done the same thing with 2 sets of rims (15x7's rubbed at full lock in reverse, went to a 15x6 and it only rubs barely on one side now) Could the manual box be worn and the tires are not turning at the same rate? Box has not been rebuilt as far as I know and the car has 87k on it. I may go with a PS set up all new in the winter. I will still check the tires for odd wear though too.

For the first red sentence, So :-), seen it brand new, and even within a day of being put on.
Big O tires for example are notorious for not being round or flat across the tread brand new.

Second sentence, No, as the tierods and those related parts handle syncronization of the tires not the steering box.
I suppose it could be a bad ball joint or tiedrod end but usually only if the tire isn't round on top of it all.