I think you will be shocked at how much you can plant in that space. I would second the suggestion of checking out Square Foot Gardening from the library.

The concept is that you divide your space into 1'x1' blocks and plant a certain number of plants in each.

I have an area that's just a bit larger (72 sq ft) than yours and I'm planning to have 5-6 tomato plants, 8 pepper plants, bush style cucumbers, eggplant, beans, lettuce, carrots, brocolli, and a variety of herbs. The key is putting some thought into how things will be planted and grow over time.

I would say you have definitely come to the right place, and that the advice to get hold of the Square Foot Gardening book (by Mel Bartholomew) is a very good idea given the space constraints you have. I would say the book is probably well worth buying for you. I refer to it regularly for plant spacing and other information. 8x8 is enough space to grow lots of veggies with the SFG method, but I would not advise trying to use all of it, as it will be impossible to reach into the middle without stepping on the soil, and not stepping on the soil is one of the reasons that SFG works so well. I would recommend a row of 12 x 12 cement pavers, stacked to the appropriate depth, in the middle. I'll see if I can make a picture, the letter s represents soil, the letter p represents pavers, the long edge with all soil for beans would be the north edge in an ideal situation. Looks like I will end up using two letters per square foot going left to right to make the diagram sort of square.

ssssssssssssssss
ssssssppppssssss
ssssssppppssssss
ssssssppppssssss
ssssssppppssssss
ssssssppppssssss
ssssssppppssssss
ssssssppppssssss

This arrangement will leave your son with plenty of space to grow things and he will only have to reach 'in' a foot and a half to reach his plants. As an only moderately tall adult I make find that 2 feet is my limit for easily being able to reach into the center of my beds without stepping onto the soil, so I stick to 4 feet as the "width" of my beds, although I have no trouble with the length being more than 4 feet.

As for the peas, I would plant at least the 8 plants that will go into a single square foot, and I would recommend 2 or 3 feet devoted to them as it sounds like you have at least 3 people who can eat them, and your current plans will produce a very small number of peas and a huge number of beans. Also, there will come a time when the heat will probably 'kill off' the peas and you can replace them with some beans that will probably produce by the end of the season (you might also be able to put in some peas in the fall 'down south' (relative to me) there). Even with the paving stone arrangement I mentioned, and 27 squares of beans and peas, at 8 plants per square. That is a LOT of beans, you might want to consider some tomatoes along the edge of the bed, or maybe not devoting three whole sides to tall crops. I would probably recommend two sides as plenty.
Anyway, I'm going off track, even with all the edges and a little of the center taken up, there is still 22 square feet left to plant in. Asparagus (a favorite of mine too) only allow 2 plants per 4 square feet, and take a couple of years to get established before producing, so I wouldn't necessarily recommend them for a garden for an 11 year old unless he is very patient and determined. Broccoli takes a square foot per plant, strawberries go three plants per 4 square feet, and sixteen carrots grow in one square foot! He could, for instance, grow 6 strawberry plants, six broccoli plants, and 128 carrots. I've put a link to the SFG plant spacing section of the Gardenweb SFG faq, where you can find the spacing for a bunch of veggies that he could try as well. If you only put the peas and beans along two of the sides that would allow another seven feet for other plants.

Again, I highly recommend the book, the authors formula for soil 'Mel's Mix' makes an excellent soil that will grow things well in the first year and into the future.

Here is a link that might be useful: SFG plant spacing FAQ