The Activity Monitor app is in the /Applications/Utilities folder.
Just to make sure you are looking in the correct folder - you would also see Airport Utility, Keychain Access, and Audio MIDI Setup, just to name a few random apps that will be in the Utilities folder.
If you have moved Activity Monitor to another folder - does Spotlight find other files? Try some other files that you know exist on the drive. If Spotlight is not working, you can try resetting the search database: Open the Spotlight pref pane, and add your hard drive to the Privacy tab. That will remove the database. After a few seconds, remove your hard drive from that Privacy tab. Spotlight will create a new database, which will take a few minutes, perhaps up to an hour.
If Activity Monitor is completely gone, you can get it back by reinstalling OS X.