Well some love Roppongi, others hate it, and most simply have not the foggiest idea what is there beyond what exists in a couple of city blocks. No news that though.
I would suggest though that with an afternoon and an evening to play with, that limiting yourself to Roppongi the entire time would be (in terms of LAX) akin to staying at a hotel in Hermosa Beach and only managing to make it all the way to Manhattan Beach duri ng your entire day there. Roppongi will be alive and well no matter what time you get back from wherever else you may venture.
My suggestion is that although the 'Pong is fun, this forum has a wealth of suggestions of options that your time frame will allow. Have a good look at the top of the forum and do a few searches to discover what can only be described as gems of ideas here.
Mike