Was there 4 years ago...…….agree not the most easiest place to just "hang out". Stayed in the Shinjuku section of the city...…...took some day tours and checked out the
Robot Restaurant and the Golden Gai which is a famous series of very small old bars along very narrow alleys. During the day the Shinjuku Gardens are very nice. I remember I wanted to sample more of the traditional Japanese eateries (which I did near Tsukiji Market) but the hotel clerk seemed to just want to direct me to touristy "American style" restaurants in the Shinjuku area. You can also get a nice massage at Erawan Traditional Thai massage in the Roppongi section where there are a lot of good restaurants and night life.