I live about 18 miles west of Southampton so am a frequent visitor. Is OK as a city, that's all I can say - not particularly picturesque as say Winchester, Salisbury or Chichester would be.
Is about 75 minutes from Waterloo (65 from Airport Parkway). I see Flybe have an increasing number of destinations from SOU too ^
And the best thing about Southampton.......Bournemouth is only 20 mins drive and the New Forest even less ^