It takes us a little less than 2 hours, going direct. A stop-off at the Space Center is a good option for a full day (leave WDW early, get to the Space Center at opening, head to VB about 3). Other plans we have had included a half day at the parks, then after lunch heading straight ot VB.
As for sights, well other than the Space Center, I think I might recommend stopping at Hale Groves about 2 miles short of VB, and a meal that Cap'n Hiram's in Sebastian, but those are kinda VB things to do. For in interesting drive, perhaps A1A from Melbourne south to the VB resort (which is actually north of Vero in Wabasso Beach). I hear that 192 thru Kissimmee is not recommended; lots of lights, traffic, strip malls...
Enjoy!