Solihull - Knowle and Dorridge in particular are very nice if you buy into the whole 'middle-class-suburbia' thing. Good schools, nice pubs, good parks...
Between Solihull and Warwick you'll find plenty of smaller villages and hamlets (Lapworth, Hatton, Honiley etc) which would suit if you wanted somewhere a bit quieter (although maybe not in HON!)
All can be quite expensive compared to the rest of S. Bham though.
Having said that, I'm looking for tenant(s) for a 1 bed brand new city centre apartment (with parking) if you're looking for short term