Old times or old time?
Solution 1:
The first sentence you wrote is the correct one.
As reported from the NOAD, Old times is used, for example, in the phrase for old times' shake to mean in memory of former times, in acknowledgment of a shared past.
They sat in the back seats for old times' sake.
Old-time is used to refer to something old-fashioned in an approving or nostalgic way (old-time dancing).