?
Given that the airport is a stone's throw away from Warwick Castle (One of Britain's top tourist attractions), Stratford & Kenilworth Castle, and that Coventry itself has a reasonably interesting tourist trail (Saint Mary's Guild Hall, Cathedral, City Walls, Spon Street, Medieval Chuches/Spires) and a couple of museums (Not to mention is well known for the Cathedral & Lady Godiva) I think it's a fairly decent "tourist" destination, especially for a weekend break - maybe longer.
Other minor "attractions" could be Leamington (Although the parade has been ruined by excessive street furniture, if you ask me) and places like Coombe Abbey, Warwickshire's manor houses, Rugby...
I'd also point the more adventurous in the direction of Coventry Canal basin and a stroll up to the Cash's Top shops (Which Sadly, lack a visitor's centre) or maybe out to Chapelfields for a "pub crawl" down the old watchmaker's district (Complete with distinctive watchmakers houses) and maybe up to Earlsdon for lunch at the "Gallery".