Can't help you with the 4x4 trails but I really envy you having your first trip to South Africa and Addo specifically. Addo is a great place to have your first taste of South African game parks. It's large enough to keep your interest but small enough to get to know your way around quickly. I think some of the larger game reserves like Kruger can be a bit intimidating due to their size.
Are you driving to the park along the N2 from the direction of Port Elizabeth? If so, you have two options. You can take the first turning off the N2 sign-posted Addo NP which takes you through Motherwell and up the Western edge of the park outside the park boundary to get to the main reception area just past the village of Addo. Or you can stay on the N2 and exit at Colchester, entering the park at the southern gate and drive through the park to get to the main reception. There is a Spar supermarket at Colchester off the N2 a bit further along than the exit you need to take if you want to stock up on groceries.
Inside the park, it doesn't really matter where you go, you can hardly fail to have great elephant sightings. In the southern section, we've always been lucky with the Mbotyl and Nglube loops. We saw this handsome chap there.
In the northern section, Hapoor dam is one of our favourite spots. We were lucky enough to see a gathering of several herds there last year. We counted over 200 elephants!
I'm sure you'll love the park.