If a 700C cant fin in there you have 3 options.

1 the frame is for 650C wheels or 26.
2 the rear brake bridge was modified but doesnt looks like it was, no idea if what u have there is a nishiki anyways.
3 You did not mention anything about the fork so i will assume the fork works fine.

Between the 3 my fav is number 1.

Sure a 700x23 will fit. The rims are 700C or you would not have been able to put the tires on the rim.

My theory, you have a 650 frame in there, the fork might not be the original either.