Personally, I felt like the mall in front of Sensoji was a giant tourist trap. The only worse tourist trap was the level of stands in Tokyo Tower (don't waste your time there). Some people don't mind the tourist traps- you can certainly find lots of gifts- but I did.

Two places for good gifts are the Oriental Bazaar (yeah, still tourist trappy, but a bit better than the other two), and the little shops in front of temples and shrines. All the ones I found were outside of Tokyo, but cool things like a little Hello Kitty in a deer costume charm specifically for Nara- that kind of thing.

Another great source of unique gifts and collectibles are- I kid you not- conbinis (convenience stores): First, there are these series of collectable toys, busts, and mini-models from popular anime series. They range from the normal (mecha and characters) to the bizzare (Ultraman dressed as a salaryman??!!). You can find similar things in 100-yen bubble machines. The second source, and my favorite, are from the plastic bottle drinks in the cooler. Pepsi has these little toys attached to the bottlecap, and they are really cute, unique gifts. On my first trip to Japan, I drank nothing but pepsi and brought home all these little PepsiMan bottle-toppers - one series was the movie monster series, and the other one, he gets into all sorts of accidents! Typically bizzaro Japanese. The next time, I drank nothing but nasty Pepsi Twist (and nastier diet), and Hajime unsweetened green tea. Pepsi Twist had all these Super Mario Bros bottle toppers, and Hajime had these gorgrous little dioramas of traditional Japanese life that connected together.

Again, those make great little gifts, you are going to want something to drink anyways, and they are very time-sensitive (new promotions every few months), so its something unique and non-touristy.