Places where I would buy a house with the criteria you listed...
Fordingbridge (North East of Poole, just within your 45min commute).
Dorchester (West of Poole, again, at the edge of 45min commute). Dorchester is a lovely town, with many small villages nearby that all have character.
Wimborne (I live here, twenty minutes North from Poole, rural market town, with many smaller areas nearby such as Colehill, Pamphill, Stapehill that are nice too)
Ferndown (slightly North East of Poole, twenty five minutes out, some very nice areas )
Most of what Whitesupraboy posted.
Bere Regis (West of Poole, again several smaller villages nearby that are nice)
TBH, a good Estate Agent such as
http://www.christopherbatten.co.uk/
http://www.alancosgrove.co.uk/
http://www.symondsandsampson.co.uk/
will be able to give you a heads up as to the nicer areas and the ones to avoid. There are many naff areas down here, close to really nice ones, it is a bit daunting if you dont know the area and only have a short time to look around.
Im sure theres a few Dorset guys on here who would give you their opinion on an area if you ask...I would:)