I've lived in Leamington Spa for 30+ years, and I can guess what is meant by "also going downhill"! It is a bit - but it's not irrecoverable and it's fair to say any descent it's experiencing is from a high peak.
Like any town its shopping is taking a bit of a hit at the moment, particularly in The Parade, our main shopping street, which lost House of Frasers a couple of years ago - it was a sizeable chunk of frontage. The site was redeveloped but is still largely unlet - I believe there were hopes that some of the computer gaming companies would move in, but it didn't happen. M&S moving their clothing store to The Shires Retail Park on the outskirts emptied a large part of the town centre Priors shopping centre too. (M&S Food Hall is still on The Parade.) On the plus side, we seem to be attracting a few new small independents and there is an excellent range of cafes, coffee shops and restaurants.
Schools in this area are good, primary and secondary. (You said your oldest was starting school next year?) We're the main site of the Warwickshire College, and there's lots of resident students for both the College and the nearby Warwick University.
Lots of parks through the centre of the town, a six-screen cinema, The Spa Centre theatre attracts lots of acts. It takes me just over 20 minutes by car to Stratford-upon-Avon if you want world-class theatre.
Is your husband working in Brum? I think it's about 30 minutes by train to New Street or Moor Street.
Have I sold it to you yet? 
Warwick is lovely too, and the two towns are frankly joined at the hip. Fewer shops and cafes, but the annual pass for Warwick Castle is worth having in the summer holidays for children. I would go once or twice a week when DS was small, he loved listening to The Bowman (tales of Agincourt) and watching the trebuchet and the occasional jousting. Take a packed lunch and it works out as pretty cheap entertainment. Warwick also has good schools.
Kenilworth I don't know so much about. Smaller than Leamington and Warwick, although there's been quite a bit of housebuilding on the edges of all three towns lately.
Leamington does still feel safe to me. There have been a few notable incidents in the past couple of years - a machete taken into the college, a rape in the park, a shooting that was gang-related - but these all stood out because they were so out of the ordinary. The sort of thing you read about in the paper rather than feel on the street IYSWIM.