Good question, friend.

It's important to note that while the North may not have had Jim Crow laws, African Americans did not often enjoy much better treatment up there either. I highly recommend Thomas J. Sugrue's Sweet Land of Liberty: The Forgotten Struggle for Civil Rights in the North. Now, it's quite a hefty tome, so allow me to briefly summarize most of its arguments:

When World War I happened, millions of blacks moved from South to North from the 1910s to the 1920s in an exodus called "The Great Migration." Oppressed, as you rightly noted, by Jim Crow and general racism in the South, blacks hoped to find good jobs and respect in cities like Rochester, Detroit, and Cleveland. (1-5)

Unfortunately, such hopes were dashed. As they moved North, many whites did all they could to make the new arrivals feel unwelcomed. City authorities drew up housing covenants that excluded blacks (6), schools were segregated and even the Klan popped up (it had spread North because it hated Catholics as well as blacks, and many Catholics had immigrated to Northern cities--pages 7-8), and most importantly, blacks were discriminated against in the job market and never enjoyed the same rise in income other groups did, even after World War II. Sugrue notes that

"despite the growth in black income, black men in the North earned only three-quarters the income of white men...Every year after 1953, blacks suffered unemployment rates more than double those of whites--a pattern that would stubbornly hold throughout the following decade. In 1962, 10.2 percent of blacks, compared to only 4.9 percent of whites, were unemployed. It was, in other words, close to a full-employment economy for whites, but a deep recession for blacks." (p. 256)

Naturally, these problems got even worse in the North in particular. Sugrue goes on to point out that Northern heavy industry, which had employed blacks during World War II, began to suburbanize during the 1960s, moving their plants to all-white areas. This happened in Detroit and NYC, and the meatpacking industry took a hit in Chicago (again, p. 256).

The effects of this were predictable. Many blacks felt their dreams for a better life in the North had been smashed, and few things make people angrier than broken dreams. The reason unrest grew in the North as well as the South (I didn't say "instead of" because there clearly was unrest in the South; after all, you did have the Birmingham march and everything protesting racial conditions there) was that blacks labored under conditions comparable to Jim Crow, even if they were unofficial. Yes, perhaps the North didn't call it "Jim Crow," but it still denied good housing, good schools, and good, secure jobs to African Americans. It reaped the bitter fruits of this discrimination in the riots it experienced during the 60s.

I only consulted one source here, but it's so comprehensive I thought it was enough :)

Thomas J. Sugrue, Sweet Land of Liberty: The Forgotten Struggle for Civil Rights in the North (New York: Random House, 2008)

In addition to /u/Gunlord500 's answer, i'd add that many organizational differences made the North/West and South different as well. More Radical organizations such as the Nation of Islam and Black Panther Party were based out of, and found their membership in cities across the North, contrasting states like South Carolina where the local Civil Rights Leadership actively prevented more radical organizations from gaining a foothold. The texture of the local civil rights movement was not only different in Birmingham compared to Detroit, but different from Detroit to Chicago, different groups, some more militant than others held sway in different areas. In addition to this, the inability to travel or relocate, rampant poverty, increasing drug and crime use were epidemic in many Northern cities, combine that with virulent racism and you've got the recipe for riot.