Is he old enough for the Reeperbahn? (No, it's not all x-rated, especially during the day)

Also, for historical purposes, I forget to mention The Old Commercial Roo, directly across the street from St Michael's Church.

From my list above, casual for a teen:

• Friesen Keller, 1 block from the City Hall (Rathaus) -- one of my favorite casual German restaurants in the city
• Sunday morning? go to the fischmarkt
• If you like watching the ships come and go, take the S-bahn up to Wedel and eat on the patio at Faehrhaus Willkomm Hoeft
• Closer in, on the harbor, Landungsbruecken high enough to overlook pedestrians
• High on the hill, overlooking the harbor, eat on the patio at Hafen Hamburg