Well, of course, the kitchen is a great place to start. Why don't you take him to the library and let him pick out a couple of children's cookbooks to check out, and the two of you can pick recipes, go shopping, and then put them together. Don't forget--while we've become jaded to the experience, a grocery store is a fantastic place to take a child--so many things you can teach/reinforce there. Look at all the produce, for example, talk about how and where it grows, how it gets to the store, the gorgeous colors and interesting shapes. And maybe let him pick out one food he's never tried to bring home and taste test. How about reading a book together then cooking something to go along with the story (Strega Nona--spaghetti salad or spaghetti pie; Cloudy with a Chance of Meatballs--do those little cocktail meatballs with the ketchup/jelly sauce--kids love them; Now I Will Never Leave the Table is good to use with those Bisquick spinach squares.)
Take a look at your neighborhood as if YOU were a visitor. There are so many interesting things to see and do in any neighborhood--the fact that he's from out of the area is great. Look for: interesting playgrounds, natural history sites (the first full dinosaur skeleton ever discovered was found about 3 miles from my house--it's fun to take kids to see the area, the placque, and then go downtown to see the life-sized dino sculputure). Not saying you have a dinosaur site in your area, but you've got something interesting. Children's museums. Zoos. Check around to see if your community theater is doing any children's shows. Is there a working farm, or other place of business that might interest him? If you want to avoid spending much--think about things like going to the local pet store to see the animals, or the science, rock or hobby shops in your area. See if the library is doing any children's activities. How about going to the local animal shelter for a morning to walk some of the dogs?
Take a penny walk through your neighborhood--at each corner, flip a coin to see if you go right or left.
Oh, and buy a copy of the book, "The Ultimate Book of Kids Concoctions". Great resource--all kinds of crafts, art projects, etc, that you can do with kids with ordinary household products. And they're all really fun--I've used a lot of those things with my summer school kids. They LOVE the activities and I've found appropriate ones for ages 4-10 in the book.
I bet anything, if you sit down and really think about it, you'll come up with more activities to enjoy together, than you'll have time to do in one visit. Have fun!