Baseball might be okay, as many of the games will be day games; and downtown is fine during the day. I am reminded of what has become of Legion Field and the area surrounding it, though... a disgrace what that area has turned into.
Of course, my girlfriend and I went down to City Stages every night last year, and we never saw or heard of any crime issues for the entire event; and we often had to walk quite far late at night to get back to our car. Shame that the event went belly up because, like almost every event or enterprise in Birmingham, it was mismanaged by frauds and crooks.
In any event, the point is, it was safe because there was always the largest police presence I've seen anywhere, for any kind of event. I suspect it would be the same for evenings when baseball games were scheduled.