Hi I'm going to spend 3 weeks in Japan on October, the first of them being all in Tokyo. I was thinking about buying a 14 day JR Pass and activate it only when I leave Tokyo and during my stay in tokyo I just pay transportation (subway, bus, ..). Am I thinking right? or is JR Pass useful to move arround Tokyo districtsand it would be better to buy a 21 day Pass and activate it as Soon as I get to Narita Airport?
It depends where you are going in Tokyo.
Generally unless you are going to some specific areas in the south west of the city, where private lines like the keio and odakyu provide most of the service (though not that much for tourists down there...), you can get by sticking purely to JR lines as a tourist. The subway and metro generally serve to fill gaps between the major JR stations, largely serving people who live and work in the city.
Transport in Japan is pretty cheap. The subway is generally a few yen more than JR lines but you are still talking less than 300 yen a journey within central Tokyo. Not something to worry about.
If the pass for the extra days in Tokyo works out at more than 1000 a day then it isn't worth your while. It's unlikely that you'll be taking this many trains in a day and the convenience of the underground railways can sometimes be nice in giving you a faster trip than sticking to the round about JR route.
If it works out to only 500 or so extra a day then it is totally worth it. JR is not at all useless in Tokyo- those famous images you've seen of subway pushers in Tokyo? They probably weren't on the subway, most such videos I've seen were from the JR ran Yamanote ring line.
I found it very useful in Tokyo, especially since it was valid on the Yamanote Line. A lot of the major tourist destinations are on that line.