There will still be plenty to do and screw with around town, but most story missions warp you to "instances," much like in World of WarCraft and other MMORPGs. Seventy-five percent of the missions in Saints Row actually take place in these instances.
That doesn't sound so great.
you can beat people up with a giant purple [censored] while wearing a furry outfit, and then make your getaway in a hover jet with laser missiles
But that sounds so awesome that I'll get it anyway.