I was born in Buffalo and lived most of my life there, if you go to Anchor Bar, do it only for the experience, not the wings, they are pretty awful, and I really wanted them not to be. Depending on where you are staying and how far you're willing to drive to get food, but you HAVE to have a Bozana's pizza, Mighty Taco, and mandatory would be Duffs. If you're anywhere near Williamsville on saturday, Bocce's pizza on Transit Road, (the REAL ONE) is also a can't miss affair.
When I come home to visit, I have all 4 of those things without fail, then head to Wegman's to get my Rooties Bleu Cheese, and Bison chip dip, and 2 sticks of Margherita pepperoni, and lastly, Weber's mustard, enough to last me a few months. If you're going to be in the area, make sure you get these essential survival items, and you'll be fine.
If Italian Sausage is something you love, Johnny's market on Hertel Ave in North Buffalo will become another Can't miss item. Best Italian sausage hands down.