Bicycle sizing is very personal, and depends on many different dimensions of your body, not just your height.
A reputable bike shop will be able to offer you a fitting service. This can ensure that you get the right size of bike, including changing certain parts of the bike if necessary.
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Do a net search for "bicycle fitting". It'll lead you to web sites who'll tell you how to measure yourself to find out which size bicycle that will be suitable for you. You really need more than your overall height to get an accurate result.
In order to correctly size a bike to you, you need to be fitted.
The bike shop will measure you and use a special "fit kit"
Throwing that all aside and just generalizing, you should be riding about a 13 - 15 inch frame if it's a mountain bike, and a17 to 19 inch frame if you are riding a road bike. Your stem and crank length will vary depending on your body.
Probably a 24" roadmaster, i tried that and i could fit on it and almost ride it (i'm not so good with bikes so that wasn't the bike being to big or to small)
probably a medium frame for a 26 in. wheeled bike (you would have to adjust the bike to one of its smaller settings. ask a store clerk for that) or a small frame for a 29 in. wheeled bike.