Most families have something that they are proud of and some link to fame, even if it's vague. Here are a few ways that you can identify the vague link to fame that your family might be over-proud of:
Ask Around: Ask your family members, in particular the older ones, about what they are proud of in the family. You may find that there is something that your grandparents, or great-grandparents achieved that your family is particularly fond of.
Check Family Records: If you have access to family records, such as birth and death certificates, you may uncover something noteworthy. Perhaps one of your ancestors was a notable figure in their home town or the subject of a small article in the local paper.
Look for Anecdotes: If your family talks about things going back through the generations, listen for anecdotes about any sort of success and note it down. It might not be something you'll find in any records but it could be something that was important to your family and that they are proud of.
Investigate Family Surnames: It could be that your family surname is linked with something that you weren't aware of. Perhaps there is a person of note in your family's past or a street or pub somewhere in your home town that bears the family name.
In reality, any person's family history is filled with stories, some of which may fall in to the category of a "vague link to fame" that your family might be overly proud of. Taking the time to investigate and research, speak to relatives and look for records, could lead to a discovery that could surprise and also please your family.