Birmingham is a great city overall with excellent transport links. There are always lots of great places you can visit and explore in Birmingham, but if you’re going to visit places like the Black Country Museum, Cadbury World, or Dudley Zoological Gardens, it helps if you drive as you can fit more into your day.
Though that being said, each of those locations is massive and it will take some time to walk around, see the sights and take part in whatever activities they have there, or just relax in the Zoological gardens and see the animals.
So it might be best to pick 2 of the places you most want to see that are close to each other and visit one Saturday and the other on Sunday.
Of course, there is also the National Space Centre and Science Museum in and around the city centre, so you can explore the heart of the city also and get even more out of your weekend break.