Well, normally the driving events at a Conclave - apart from the competitive events such as a gymkhana, a "funkhana," and perhaps a rally and even the occasional hill climb - usually consist of some organized tours to local attractions, self-guided tours where groups of people get together and drive to local attractions on their own schedule, and the trip to and from the event. There are usually organized groups of cars traveling to the event, and a post-Conclave tour that you can join in.
That said, like pretty much ALL car club meetings, it is fundamentally a social event, and so there is social time and group meals in the schedule.
It's perfectly acceptable to spend as little or as much time there as you like. If you plan to combine the trip with family visits in the area, you should be able to schedule things so that you can make whatever elements of the event you like best. The car show ("Popular Choice" or "People's Choice") is usually a highlight - it's a relaxing time with lots of cars and lots of people, so most people really make a day of it. Bring a couple of folding chairs if you like.
Since you've never been to a Conclave I would just add that they can be addictive. At first you might be hesitant to go, but after you do go to one, and you meet some people, and you see and participate in the fun, it's very likely you'll want to get to all of them.
I hope to you see there!