Hey Jason,
Caesars is a pretty good casino and is centrally located at the end of the expressway on the boardwalk. I personally like Harrahs' casino better but the location is on the marina. But those two casinos are very good so I wouldn't hesitate to recommend either. Children are not allowed in the gaming areas, but those are delineated pretty well and there shouldn't be a problem with your children.

In general the boardwalk is fine. Like you said there are some areas I would avoid but right where Caesars is has plenty of shopping (the Pier on the boardwalk side and the Walk on the street side) so there are usually plenty of people and you shouldn't have any problems. Like always be aware but I've never had an issue.

Caesars is surrounded by the shopping I mentioned, the shuttered Trump Plaza, and Bally's. Its a quick connector to get over to Bally's indoor (or via the boardwalk) so there will be plenty of food and shopping options as well.