DON'T shop around this area i.e. Asakusa. The souvenirs here are exhorbitantly priced. DON'T shop at major department stores too unless there's a MAJOR sale going on. If you can, refrain from shopping in Tokyo. EVERYTHING COSTS A BOMB HERE!
My buddy bought a Max Factor lipstick that would normally costs next-to-nothing in the U.S.A.; but in Tokyo, she paid US$21 for it at Tobu Department Store! (Gulp). If you reeeeeally want to shop and bring something home to your friends and family, I suggest you visit those 100 Yen shops. You can find them sprinkled all over the city of Tokyo. It's a better bet and believe me, you won't have to live on bread and water for the next 2 years when you get back home (read: paying off those credit card bills!). :-))
P.S. Please note that these 100 Yen shops DO NOT accept credit cards. Cash only.
Though not really a 'trap', the Nakamise Dori leading up to the Sensoji Temple is worth a trip, but probably not two (too crowded).