There are lots of old bikes out there, but what do you intend to do with it? Generally older bikes were well made, but not all are suitable for an in frame motor if that's what you're thinking. Get an idea of what appeals to you. I'd suggest spending some time on eBay to look at pictures and be able to ask sellers questions. On ebay look up offerings for pre war (meaning WWII) bicycles, balloon tire bicycles, Monarch, Elgin, JC Higgens are just a few. Old Roads is a vintage bicycle site on the net where you can look at pictures and ask questions. Go to the library and see what you can find. In other words, become informed. A good way to buy an old bike is to buy just a frame of one which appeals to you. Then buy new wheels, new handlebars, seat, whatever... it will still be an old time bike because of the frame. It is like someone with an old 32 Ford they want to make into a hot rod. They change the engine, the rear end, front suspension, transmission, reupholster, chop and channel or whatever... it is still a 32 Ford. Same with your old bike. I hope you end up with exactly the bike that rings all your bells. Good luck and let us know what you find. It is like treasure hunting, only better since you get to build it and then ride it and by then it is all yours.
Silverbear