I used to use a dedicated report for this, but it was a long time ago. JIRA doesn't directly track "project create" or "project last used" dates (well, the audit log traps created projects now, but that can be cleared and often doesn't go back far enough)
So I used a hacked-together report which gave me the project ID (database id, not key), and last issue number allocated with its updated date. The project ID lets you put them in order of creation, and the last issue updated usually gives you the last time the project was used. This was ok for me, because we were looking at "empty" (last issue number very low or not even there) or "over a year old" (it's rare that an active project will have updates but no new issues)
It could be more clever - ideally it should have read "earliest created date" and "latest issue updated date", but I was in a rush and never had time to do it better.
To do it in sql, read the project table for the raw project data (highest issue number and key), then you should be able to construct "find oldest created and newest updated" queries on to jiraissue.
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