Wyoming.
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.
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.
Yes, Pakistan is a nuclear state, and it is growing its nuclear arsenals day by day.
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.
Narora Nuclear Power Plant is located in the state of Uttar Pradesh, India. It is situated in the Bulandshahr district along the banks of the Ganges River.
Illinois has several nuclear power plants (see link below) with a total generating capacity of 11,263 MWe. I don't have details of other types of power plants in the state.
Which country/state is it in?
Yes, both in power generation and weapons.
Australia, New Zealand, and Italy use zero nuclear power
Colorado is a state in western USA