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Laura, that's a good idea.
I had to do the same thing at the SLC airport last year. I was flying in for a ski trip, the boyfriend was flying in a few hours later, and the people already there were only making one trip out to get us. I was worried about someone taking my snowboard bag so I left security right away.
There is a snack bar outside of security that sells pretty good sandwiches, but there are a number of tables set up in front of it where you could eat a to-go meal from a restaurant inside security. Other than that, there isn't much.
I think you should see if you can have a pizza delivered to the passenger pick-up area outside the terminal :)
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Maybe you can get your luggage and ask the customer service people for your airline to hold it for a few hours while you wait for your relatives. That way it would at least be in a secure area. I don't know if they'll do it, but it's worth asking so you don't have to schlepp your luggage around with you for hours.