If you want to stay on the city side (lots of restaurants and shops) definitely pick a place near Shinjuku, Shibuya, Ikebukuro, Ginza/Yurakucho. There are many restaurants and bars open until night in this area even on Sundays.
If you can't find a listing in this area, any stations in JR Yamanote Line are convenient. JR Yamanote line is the latest train line to end operating in Tokyo and all of the area above (Shinjuku, Shibuya, Ikebukuro, and Ginza/Yurakucho) are located within Yamanote Line. So you can get to your apartment even after going out at late night.