I was born in the country and grew up in Leam, as did my husband. Whereabouts are you looking? It is made up of a lot of small villages joined on around the town (IYSWIM) as the town has grown. My family don't live there anymore but the IL's do. I think some of the edgey bits can be quite insular (in a 'all my family lives in the next few streets' kind of way) but that's not necessarily a bad thing.
It isn't dull and suburban for the most part, Warwick University is a short bus ride out of town so it can be a bit of a student town, lots of pub/winebar type nightlife.
I don't remember a huge amount for younger kids to do, but I was 9 when I moved there so I wouldn't have noticed it anyway. The schools are all quite good and the countryside is right there so it is easy to go from centre of town to nice parks outside town. Also jephson gardens has some great ducks! There are fairs and stuff that visit too for kids, nnot sure how often now though
With regards to culture you have the Spa Centre, the loft theatre, and also stratford and warwick are in easy reach with shakespeare stuff and the castle. The globe theatre is in stratford and cos of the student population you get quite good gigs and shows from tours going to coventry and warwick.
It is a lovely place to grow up but it is quite slow, I have lived in liverpool and madrid and leam is easily quieter than them, but it is a large town, not a city.
I would go and spend a few days there if you could, especially take a wander around the suburban bits. I can't comment on teh whiteness of it as, being white, its not something I have noticed. I know there is a large pakistani population, probably a third of my class were pakistani but there were only a few black children at my entire school, but times may have changed, I don't know.
Hope that helped! Got a bit waffley, sorry!
Off to bed now but feel free to ask on!