Well we are in Birmingham and thinking of travelling to Manchester for the BBC studio thing - have you looked at that?
Anyway in Brum (2hours in car)
Science museum at Millenium point - right in city centre. Has huge intestine,heavy machinery from yesteryear, interactive stuff, toddler zone, outdoor picnic area with scinecy type puzzles. It has a cinema and a planetarium. I would say full days worth. Different ticket combos availabel but also accept tesco vouchers.
Cannon hill park: crazy golf, lovely well kept flower beds and trees, squirrels, ducks, playground x2. Inside is also a cafe, the Midlan Arts Center (they do bookable stuff for kids during hole) have nice cafe also, cinema. At the end of the park is the nature park like a mini zoo, small animals but enough, has a cafe and picnic area. It is only £5 ish.
Conkers is ok, again tesco vouchers.
I know it is further but advance tickets to London to goto free scinece and natural history museum?