New York City earned a name for itself—Silicon Alley—as a home for digital start-ups in the late 1990s, but tech entrepreneurship in the city cratered after the dot-com crash in 2001. Now tech startups are growing again in the Big Apple. Law firms are taking notice.

Between the first quarter of 2008 and the first quarter of 2013, the New York area saw a 24 percent rise in the number of venture capital deals, while tech hotbeds Silicon Valley and New England experienced declines, according to a study by the Center for an Urban Future. A report by PrivCo, a business and financial research company, ranked New York just behind Silicon Valley in the number of locally based tech companies being acquired in 2012: more than 100, worth a total of $8.3 billion, compared to 226 acquisitions worth $21.5 billion in Silicon Valley. New York's Shutterstock, a stock image business, went public in October at a valuation of $558.3 million; New York's Tremor Video, a video advertising company, followed in June at a $470 million valuation.