Please Shel, it is not that bad. People used to say same about Redfern and it is a highly sought after suburb now. Bankstown used to be a bogan/refugee/welfare suburb. This is quickly changing as wealthier neighboring suburbs push “the undesirables” away.
If you are a female avoid staying there till late and both you and your husband, avoid local clubs and pubs. They are just a bit too rough. Otherwise there is no problem. During the day it is business as usual. It is probably a suburb with one of the highest crime rates in Sydney but it’s nowhere near comparable suburbs in America. You still can safely walk around during the day.
Bankstown has excellent train network so it is easily accessible from anywhere in Sydney. I wouldn’t necessary leave there, as I value my night walks and ability to pop into any club or pub I see on the way. Plus you would probably want to walk your kids in parks and have a beach not that far away. If you can tolerate the commute (about 40 min on train) St Peters, Marrikville and Tempe are close by, safe, clean and entertaining. On the other side of Sydney, Homebush and Rhodes are a good call (close to train stations and virtually no crime, water nearby).
Depends on your financial situation eastern suburbs are absolutely the best; they are the gold standard of Sydney. But they are pricey, and locals resist trains furiously, so you’ll need to travel by bus to the city (approx. 30-45 mins) and catch a train to bankstown.
In general Sydney works this way (East and North, good/safe/cafes and everything else. South a mix of good and bad (the further south the better), West not so good, the further west you get the worse it gets.)