20mm is about the nominal size for a road rim, though they do come in different widths. Most tires are pretty accomodating. Are you sure you are working with the right sized tire? That Miyata is an older machine (I have a Pro-Miyata myself) and could concievably have 27" rims. If so, you would struggle very hard indeed to get modern 700c tires on same....

Even if everything is correct, road tires are generally a little more difficult that MTB tires. You can certainly go to a wider size than the 23s, limits being your frame and/or brake clearance. Road tires are available in many widths, though the largest you see on most conventional roadsters are 28mm or so.