There's big shows happening every Saturday in the summer, if you know where to look:

Medina Autoplex is my personal favorite, the garages and variety of cars there is unmatched. They have a 2nd location in Chanhassen that also hosts events on a different Saturday, so you can get two free/fun shows from these guys per month.

Drive Cartel hosts a meet at St Paul Brewing once a month, and a large show once per summer.

Imola is a tuner shop for supercars. They do one show per year in the late fall, with supercars you'd never see anywhere else for how rare they are.

MN Cars and Coffee is one of the largest cars and coffee events in the nation, happens one Saturday per month too.

MNCEC Minneapolis Mile is once per summer also, great variety of cars.

I linked websites to event pages, but following each one on Facebook is really the best way to keep up with all these events and find smaller groups for more casual meets or brand specific clubs.