Of American-English origin, the noun Nimby (also NIMBY, nimby) denotes opposition by nearby residents to the siting of something that they perceive as unpleasant or hazardous; it also designates a person holding such an attitude.

Pronounced /ˈnɪmbi/, it is an acronym from the initial letters of not in my back yard.
—Cf. also the noun YIMBY, acronym from the initial letters of yes in my back yard (also of yes in many back yards).

Because this is the earliest quotation in the Oxford English Dictionary (3^rd edition, 2003), it is widely said that Nimby first appeared in Hazardous waste, by Emilie Travel Livezey, published in The Christian Science Monitor (Boston, Massachusetts) of 6^th November 1980:

People are now thoroughly alert to the dangers of hazardous chemical wastes. The very thought of having even a secure landfill anywhere near them is anathema to most Americans today. It’s an attitude referred to in the trade as NIMBY—“not in my backyard.”

I have, however, found earlier occurrences of the word:
– used in the phrase the Nimby syndrome,
– referring to the disposal of nuclear waste,
– from the Daily Press (Newport News, Virginia).

1–: The earliest of these instances dates from Tuesday 13^th February 1979:

Radioactive Waste
National Regulations Needed

Williamsburg — Comprehensive national plans and regulations are required to ensure the safe disposal of radioactive waste, a radiation expert said here Monday.
“The experience of the past three decades or more has been primarily that shallow-land burial has really been quite good, but this doesn’t mean we can rest on our laurels,” Joseph A. Lieberman, a member of the Atomic Energy Commission for 20 years, said.
“We need better ways to cope with institutional problems in presenting this issue to the public and to ensure state and local officials are effectively involved in locating these facilities,” he said.
Lieberman gave the keynote address to nearly 500 health physicists from government, industry, education and hospitals meeting in the Fort Magruder Conference Center to study the technical aspects of low-level radioactive waste disposal.
“The problem is one that technically we know how to handle,” but agencies need to be better coordinated and the “nimby” (not in my backyard) syndrome must be eliminated.

2–: The second-earliest uses of Nimby that I have found are from No One Wants Backyard Nuclear Dump, published on Sunday 29^th June 1980:

Some call it the Nimby Syndrome.
That’s Nimby, as in “Not-in-my-back-yard,” which is where everybody wants to put a Virginia dumping grounds for low-level nuclear waste.
Nuclear waste disposal sites in some states are slowly closing their doors to shipments from outside their borders, so Virginia and most other states are faced with a need to set up their own dumps.
The alternative is to shut down nuclear power plants, stop nuclear research and call a halt to nuclear medicine.
As director of the state Solid Waste Commission, Susan Dull has been a victim of the Nimby syndrome in conducting public workshops on the need for a nuclear trash dump in Virginia.

First used by the promoters of the projects to which the local residents object, the word Nimby has negative connotations, the persons who oppose such projects in their own neighbourhood being accused of raising no such objections to similar developments elsewhere. But, in a letter published in The Journal (Newcastle upon Tyne, Northumberland) of Monday 8^th April 1985, Bridget Gubbins, Press Officer of the Druridge Bay Campaign, refuted this accusation:

Worried inhabitants of the Weardale region who fear the Pennine moorlands may become a nuclear waste dump site are yet more potential victims of the nuclear industry. That industry is fond of accusing those who react strongly when their own immediate vicinity is threatened as affected by the NIMBY syndrome (Not In My Backyard), as though that implies indifference to wherever else may be threatened.
Here in the Druridge Bay area of Northumberland, people feel personally threatened too. So did the citizens of Billingham. Those of Orkney and Elstow in Bedfordshire still do. In fact, with nuclear expansion which the CEGB¹ hope will follow approval for Sizewell B², very few areas of Britain will not be under threat in one way or another. Once people’s awareness is thoroughly aroused as to the nature of the nuclear threat, local concern tends to spread to a wider concern, and the citizenry becomes better educated.
[…]
Rather than look down on NIMBY reactions, we would say: NIMBY here, NIMBY there, NIMBY, NIMBY everywhere.

¹ CEGB: Central Electricity Generating Board
² Sizewell: a village on the Suffolk coast, the site of two nuclear power stations

The derived word Nimbyism denotes the practice of objecting to something that will affect one or take place in one’s locality; the earliest instance that I have found is from an editorial titled NIMBY? Pipe down, published in The Home News (New Brunswick, New Jersey) of Thursday 10^th March 1983:

The whole point of the Hazardous Waste Facilities Siting Act, approved by the Legislature in 1981, was to ensure that processing, storage and disposal of toxic wastes in New Jersey would be subject to strict, safe and effective controls. To that end, the act established elaborate procedures and multilayered review processes, all designed to determine where hazardous wastes could be safely processed. The Legislature that enacted the siting law recognized […] that a single authority had to be empowered to make the critical and controversial siting decisions — or New Jersey’s need to make provision for safe and adequate toxic waste facilities would fall victim to the Not-In-My-Back-Yard mentality.
It was unrealistic to expect that the siting act would prevent outbursts of NIMBYism altogether. But the current hue and cry — before the commission has even established siting criteria and months before it will be in a position to accept formal applications for hazardous-waste facilities — is particularly disappointing and dangerous.