I will speak to the birth of Silicon Valley, because that sets the stage for the West Coast developing into the technological hub that it is today, and answers your question of why that hub didn't emerge in established eastern industrial centers.

The time frame to consider is post-war 1940s and 50s, and the key player is Stanford University. For much of the 20th century Stanford had encouraged and financed substantial research activities in order to provide a regional prominence to the West Coast more generally and to its area of California, and this primed the area for the emergence of a well-funded industry. It was not certain what this industry would be until the post-war period and Frederick Terman became dean of engineering and provost at Stanford. In an effort to provide a well-established, regionally-unique industry to the Valley, Terman actively encouraged the shining starts of the department to go out and found their own businesses, rather than stay behind in university research. Additionally, in order to facilitate easy establishment of these companies, Terman formed the Stanford Industrial Park, a scheme by which the University leased its land cheaply to these new projects (simplifying the financing of starting these companies). These elements together created fertile ground for the birth of Silicon Valley, as much as they marked the geography of where it would be, and led to the birth of, for example, Shockley Semiconductor.

Another situational factor must be discussed, and this takes place on the East Coast. You're absolutely right to point out that areas like New York, Chicago, and DC/Baltimore all were significant (perhaps, the most) industrial centers of the US, but as a part of their prominence and maturity, there unsurprisingly developed relatively inflexible channels for research funding, as well as bulwarks of established institutions and personalities that, by the nature of proven success, resisted innovation and change.

The most relevant instance of this is Bell Laboratories resistance to William Shockley, the man most responsible for the success and mass production of the semiconductor. Shockley’s professional style and creative vision put him at odds with Bell management, and an alignment of actors and events eventually led him to that fertile ground in the nascent Silicon Valley.

There can be much more discussed here, but the essentials are here: Shockley raised up a tight-knit group of young geniuses who eventually defected themselves, most noteworthy among them being Robert Noyce, co-originator of the microchip and co-founder of Intel. The distribution of those men to other companies brought about the true explosion of innovation that made Silicon Valley what it is today. In short, Silicon Valley and the West Coast technological hub emerged from a confluence of creative and industrial vision, a culture and environment without established in-networks and therefore open to change and creativity and lacking in institutional memory and inertia, and the coming together of some of the most intelligent and creative minds in recent history.

Sources

Stephen B. Adams, "Regionalism in Stanford's Contribution to the Rise of Silicon Valley"

The Stanford Research Park: The Engine of Silicon Valley

Marvel Castells, The Information Technology Revolution

EDIT: superfluous words removed

AnnaLee Saxenian explored this in her book Regional Advantage in which she compared Silicon Valley to Boston and discovered that the illegality of non-compete agreements in California gave Silicon Valley a huge advantage. Tech businesses in California were dynamic because employees were free to go where their talents were needed, including starting their own businesses. While businesses in Boston were stagnate.