Sudbury Museum of Childhood is good. National trust, stuff to do and play with inside, good adventure playground outside, nice cafe (but gets v long queues).
Trentham gardens and Monkey park. Nice gardens, good playground, barefoot walk (with squishy mud at one section, my 4 yr old loved it) and then a separate enclosed monkey park nearby.
Sea life centre in Birmingham, been with DD when 1 & 3 and she enjoyed both times.
Twycross zoo.
Conkers (maybee better for older children).
Whereabouts in the midlands would you be based?