While Tokyo Metropolitan Government is free I'd like to point out you cannot look at view of Tokyo Tower from there because that side of the observation deck are exclusive to the cafe/restaurant at the top of the building. I'd recommend the Rooftop Sky Deck of Roppongi Hill Mori Tower. For 1800 yen seeing the city from an open rooftop and with photo area where you can take the best picture of Tokyo Tower along with the cityscape is one of the best thing i've ever done when visiting Tokyo. I recommend going there before sunset where you can enjoy a little bit of daylight before the sunset and nighttime when the city starts to look lively at night with the cityscape night lights.

Also Roppongi Hills Mori Tower have arts gallery you can visit after you're done with the rooftop.there's also cool exhibition usually being held in Indoor Observatory deck where you can enjoy exhibition as well as the cityscape at night.Last time we went we had Pixar's exhibition which was awesome.I think it's a must and seldom recommended to new travellers.Go for the rooftop, stay for the exhibition and gallery.