Kudos to Belinda Hixon to include our kids in our (adult) vacation to Vegas.
When my kids were too young to participate in adult activities (don't over read this), I would take them to the Circus Circus and NYNY midways, Ethel M Cactus Gardens (free chocolates), Boulder Dam to straddle the state line, and all the strip attractions.

Add to this list of collectibles that are kid-age appropriate.
For example, chips are not because kids can't get them at the cage or tables.

Room Keys - separate the ones from where they stayed, add non-Vegas vacation hotels to the collection

Pressed Pennies - several casinos have them, and other vacation spots like Disneyland

Postcards - pretty pictures don't have to be of buildings, can be attractions, Paris tower, Luxor light beam, NYNY roller coaster, TI pirate ships, Bellagio gardens

Midway game points - keep one ticket from each casino midway

Napkins with name imprint

Shot glasses with casino names (not Slot glass) - my kid has a nice collection from different vacation spots

Playing cards - decks or singles (Belinda can make a game of this, maybe bingo like, and the kids can trade singles, each kid can start with one or two decks. Each kid could pick his favorite number/suit)

Encased cents are a stretch because most/all are not available from the casinos, but from dealers.

Kids want to have fun when on vacation too...the pool and cable tv may not be enough.