Woodville is still a good place to go to, but there are quite a few rental properties where residents could be dodgy or too loud, disruptive, ect. It may not be as safe as it used to be but it isn't bad. Close to the shops, Arndale Shopping Centre only just down the road on Torrens Road, Westfield West Lakes at West Lakes 10-15 minutes away and the CBD 25 minutes away. I have a close relative living in Woodville (Woodville West) and thinks it's not bad.
Your main concerns living here is most likely going to be safety or rental properties with some domestic fights, but other than that, a quiet and friendly-ish to live. Any other questions, let me know.