The adjective bygone is good for describing long-ago times. Your grandparents might enjoy looking at old photo albums and reminiscing about bygone days.
A bygone era happened in the distant past, and a bygone sweetheart is an early romantic interest remembered by someone who's since lived a long life. You're most likely to see the phrase "bygone days" being used in a nostalgic way. If someone says, "Let bygones be bygones," they want to make up for long-ago slights and arguments, leaving them in the past where they belong.