As one who live in the west and in a country that is part of NATO, how do the Russian people think about the placing of US missiles in some of the old USSR countries. Also as a westerner I would like to see Russia a part of NATO , what are your views?.

As a Brit, I can't see the use of NATO anymore.
It was created after WWII, to 'protect' Western Europe against the Soviet threat.
NATO was in fact another branch of the Pentagon, to protect US interests and allow them to keep a foothold in Europe.
In the battle of the superpowers, the Soviets had the Warsaw Pact, the USA had NATO, each controling their satellites or 'client states'.
Well, I never believed in the Soviet threat anyway, but now that the Soviet Union doesn't exist, NATO cannot justify its existence.
The Americans are now using NATO to further their imperialistic aims in the Middle East in a role for which it has never been intended. NATO provide support votes at the UN and canon fodder for US military adventures worldwide.
NATO is also a political tool used to encircle and isolate Russia by giving membership to ex-socialist countries around Russia, and using them in their anti-Russia propaganda.