The chief reason was to protest the Vietnam War. Planning was underway in 1967 and at that point, LBJ was still the presumptive nominee and seeing as how he was the biggest escalator of the war, raining on his parade was going to be a bonus. LBJ dropped out of the race before the DNC after nearly tying the New Hampshire primary with McCarthy, the antiwar candidate, but a lot of anti-war groups had already promised each other to show up so the mission also became to support McCarthy, not just protest the war. It became even more critically important for them to do something because McCarthy's chief rival was vice president Humphrey who favored the status quo with Vietnam. Besides, as the opposition party it was expected that Republicans would de-escalate if not stop the war altogether. Nixon even mentioned that we were "tied down for four years in Vietnam with no end in sight" during his acceptance speech at the RNC in Miami and during the general election he ran TV ads linking Humphrey with Vietnam.

Combined with Chicago's large population, multiple universities, central location, and status as a major transportation hub, it was simply going to be easier for protesters to gather a large population there, as opposed to Miami's smaller size, older population, and more remote location. Besides the ball was already rolling well before the convention got started so even though LBJ was not running it was still going to be easier to do it in Chicago.

From what I understand, the RNC chose its convention site, Miami Beach, specifically because of the remoteness and difficulty of bringing lots of protesters there. Chicago, on the other hand, was the meeting point of rail, bus aned air lines; it was full of universities and the convention center was basically in the heart of a neighborhood where Saul Alinsky had learned community organization.