One of my friends studied in NLSIU Bangalore, before that she lived in Bangalore for 28 years. According to her, the first thing to mention is yes, it is absolutely safe.
Do not get influenced by the media when they talk about a certain place, there could be other intentions for claiming that. But as she lived there she knows that it is perfectly safe for women.
The location might make you feel lonely because the campus is next to Bangalore university and there are few other central government offices. On the other side, it is completely residential.
The culture of Bangalore is very welcoming and it has given homes to lakhs of people coming in from other states and it is capable of delivering a good livelihood.
It is suggested that you do not come to any conclusion just by information provided in the media. Analyze every aspect and make your decision accordingly.