When and where was the first "computer" invented?

Seldom, if ever, in the history of technology has so long an interval separated the invention of a device and its realisation in hardware as that which elapsed between Charles Babbage's description, in 1837, of the Analytical Engine, a mechanical digital computer which, viewed with the benefit of a century and a half's hindsight, anticipated virtually every aspect of present-day computers.

http://www.fourmilab.ch/babbage/

Who invented the computer?" and when is not a question with a simple answer. The real answer is that many inventors contributed to the history of computers and that a computer is a complex piece of machinery made up of many parts, each of which can be considered a separate invention.

1951 - First commercial computer & able to pick presidential winners.

You can find a timeline here:

http://inventors.about.com/library/blcoindex.htm

Originally, the term "computer" referred to a person who performed numerical calculations, often with the aid of a mechanical calculating device or analog computer. Examples of these early devices, the ancestors of the computer, included the abacus and the Antikythera mechanism, an ancient Greek device for calculating the movements of planets, dating from about 87 BC.[1] The end of the Middle Ages saw a reinvigoration of European mathematics and engineering, and Wilhelm Schickard's 1623 device was the first of a number of European engineers to construct a mechanical calculator.[2] The abacus has been noted as being an early computer, as it was like a calculator in the past.

https://en.wikipedia.org/wiki/Computer

Charles Babbage was the first to conceptualize and design a fully programmable computer as early as 1820, but due to a combination of the limits of the technology of the time, limited finance, and an inability to resist tinkering with his design, the device was never actually constructed in his lifetime.

The first computer was the abacus. The first true tube computer was the ENIAC (1946). The first Transistor Computer was in 1947. The first "Micro Processor" based unit was not until 1970.

"The transistor is an influential invention that changed the course of history for computers. The first generation of computers used vacuum tubes; the second generation of computers used transistors; the third generation of computers used integrated circuits; and the fourth generation of computers used microprocessors."

http://inventors.about.com/library/blcoindex.htm

Charles Babbage

https://en.wikipedia.org/wiki/Computer

Charles Babbage, an English mechanical engineer and polymath, originated the concept of a programmable computer. Considered the "father of the computer",[4] he conceptualized and invented the first mechanical computer in the early 19th century. After working on his revolutionary difference engine, designed to aid in navigational calculations, in 1833 he realized that a much more general design, an Analytical Engine, was possible. The input of programs and data was to be provided to the machine via punched cards, a method being used at the time to direct mechanical looms such as the Jacquard loom. For output, the machine would have a printer, a curve plotter and a bell. The machine would also be able to punch numbers onto cards to be read in later. The Engine incorporated an arithmetic logic unit, control flow in the form of conditional branching and loops, and integrated memory, making it the first design for a general-purpose computer that could be described in modern terms as Turing-complete.

The machine was about a century ahead of its time. All the parts for his machine had to be made by hand - this was a major problem for a device with thousands of parts. Eventually, the project was dissolved with the decision of the British Government to cease funding. Babbage's failure to complete the analytical engine can be chiefly attributed to difficulties not only of politics and financing, but also to his desire to develop an increasingly sophisticated computer and to move ahead faster than anyone else could follow. Nevertheless his son, Henry Babbage, completed a simplified version of the analytical engine's computing unit (the mill) in 1888. He gave a successful demonstration of its use in computing tables in 1906.

The answer very much depends on the definition of "Computer". Charles Babbage certainly made the first of what most people would call a computer, the acabus has been around since at least 2400 BC, and an even more primitive form, a tally stick was used 30,000 years ago. Hero of Alexandria (C10 - 70AD) came up with a programmable handcart was probably the first nameable person to have invented a computer like device.

Claimants on the other side of Babbage's difference engine of 1833, we have Lord Kelvin's analog tide-predicting machine of 1872; Alan Turing's description of one in 1936; Konrad Zuse's Z3 that was the first working electromechanical programmable, fully automatic digital computer in 1941; or possibly the Colossus computer of 1943 designed by Tommy Flowers.
Take your pick

https://en.wikipedia.org/wiki/History_of_computing_hardware

We could argue that the first computer was the abacus or its descendant, the slide rule, invented by William Oughtred in 1622. But the first computer resembling today's modern machines was the Analytical Engine, a device conceived and designed by British mathematician Charles Babbage between 1833 and 1871.

https://science.howstuffworks.com/innovation/inventions/who-invented-the-computer.htm