Did you just choose the Reinstall OS X option without erasing the OS X volume first? If you want to do an erase and reinstall, see http://support.apple.com/kb/PH11273.
If you did an erase and reinstall, it might be the same issue I had with my MacBook Air. The used disk space was shown to be about 100 GB but the sum of the sizes of all files was about 80 GB. The extra 20 GB was classified as "other" in the About This Mac window and as "hidden space" by DaisyDisk:
When I tried verifying the OS X volume in Disk Utility, there was an error about an invalid free block count. I was able to get rid of the error and free up the disk space by starting up from the recovery partition and repairing the volume.
Another way to find large files is to enable calculating all sizes and sort files by size in list view in Finder: