There are many ways to spend meaningful time with the kids in your life. Simple things like reading, walking and talking are the most important ways to bring you closer together. And best of all, these three things can be combined together while sharing a hobby, such as collecting.
They've probably already expressed an interest in your collections, perhaps you can "share" some duplicates or extras. Beside the pleasure you get from sharing, wouldn't it be nice to know there is someone to pass your treasures onto. Someone that will cherish them as much as you do?
When my son was young I always took him to the flea markets/antique shows. Poor kid didn't have a chance! But I always gave him a few dollars at the beginning and he would start his search for treasures while I looked for my goodies. He would usually wind up getting some sports cards, an action figure or perhaps his favorite -- a metal bank. The upside is that he learned to spot my advertising tins and cookie jars, many times before I did. It's always nice to have an extra pair of eyes, especially those on a lower level than yours!
It's hard to figure out what sparks the passion between a collector and collectible. Your youngster might need a little spurring on here, what do they like to do? Sports -- lots of related collectibles. TV/Movies -- also lots of related collectibles with actors and shows. Cars -- metal diecast are fun to collect. You get the idea, figure out what they like and there will be something related that can be collected. It doesn't matter if it's valuable or considered "collectible" this is about fun and sharing time.
Some other suggestions might be:
State Quarters and/or state quarter bears
Travel souvenirs such as snowdomes, smashed pennies, rocks
Holiday ornaments (Larry Fraga stated at age seven!)
The list could go on forever, there is always something fun to collect. And something that will help bring you together not just today, perhaps it will be the start of a lifelong passion that the two of you can share.