My plane lands at 6am and my next flight isn't until 1pm. I'd love to see what I can and eat some local food. Any suggestions?

What day of the week?
You have to go through security/customs in and out. You have to get to and from the city centre. By train it takes around 15 to 25 mins depending on train service. Plus time for ticket purchase.
Not much will be open early hours so take the opportunity to wander around a city waking up. Then head for a coffee and a bite to eat.

Will your luggage be checked through? If not, dealing with that will take a time, and you need to be clear about when you need to be back through security and at the boarding gate. It may not be as long as you think.

You might just have time to do a sort of round tour by tram: train to Central Station, then down to the Concertgebouw by either tram no 5 (going one route) or the 16 or 24 (which go by another route); and the alternative route back.

There is actually quite a bit of local food at the airport and it is no worse (or better) than what you would find in central Amsterdam. In addition, the Rijksmuseum used to maintain a small museum right at the airport. I'm not sure if it is still open, but if it is, you might find it worth your while.

Thanks for the tips! I'll be there on a Friday and my luggage will be checked. I was wondering if much would be open that early, but I love to walk!