In the US there are many states that have no nuclear plants, Colorado, Nevada, New Mexico, Utah, and so on. (I am talking about nuclear power plants, not research facilities). See the NRC website www.nrc.gov for maps and details.
Denver Colorado
There are many states without nuclear power plants, mainly in the West, like Colorado, Nevada, Utah. See the link below for a map showing where the plants are and which states are blank.
Japan has nuclear power plants but no nuclear weapons
No. As of 2012, there are no nuclear power plants located in the state of Montana.
Nuclear Power can be used in any weather conditions
Illinois
There is only one nuclear power plant in Vermont, which is the Vermont Yankee plant in Vernon. Vernon is in the southeast corner of the state.
Illinois
Which country/state is it in?
Yes, both in power generation and weapons.
Australia, New Zealand, and Italy use zero nuclear power