There are 400 Riddles for Batman to Solve in Arkham City (in addition to 40 for Catwoman), whether it involves Collecting Trophies, lining up symbols or looking at various nostalgic Batman set pieces. The more you solve, the more Hostages you can attempt to save.
Games Radar has a guide for all of these which is extremely useful since it breaks down everything by type and has a map to accompany it. But before you can get the location of these in-game, you must start here:
Go to the Church after going through the Steel, and solve a Riddle inside. Afterwards, you’ll go to the Courthouse and rescue a hostage. There, you'll get a device that will allow you uncover the location of the next hostage. Take note that these opportunities come up after solving a certain number of Riddles, except for the first one which you have the chance to save right away.