While I can find prices for today's warships, its difficult to find prices for warships fifty years ago. I would suggest surfing the web of some newspapers and read their archives, if any are available. Its easy to find lists of warships, what their weapons were, their size, etc., but its difficult to find their price unless you search the archives at their launchings and commissionings dates, and news clips of those days or the next days newpaper clippings. Usually a newspaper prints their price. This is a lot of research, but its what the world wide web is all about.
Another route would be to read the Congressional Record for US ships prices the date of the defense appropriations bills or the day after. Either fly to Washington, D.C. and search through the Library of Congress or drive to Bonham, Texas and search the fine collection of Sam Rayburn's Congressional Record.
The US Navy League's Seapower magazine mentions price of ships expecially in their May issue, try to find their archive on the web or if you must go to a library which may have an archive in a navy town such as San Diego or Norfolk.