I have stayed at Hostal Chelo (off Gran Vía) numerous times. Several times I have been alone and the last time I stayed there with 2 of my kids. I have had no concerns about safety. However, I am always cautious at night and I do not usually stay out 'till the wee hours of the morning. The same safety rules you would use in any location apply in Madrid. I female and like staying at Hostal Chelo because I believe they would notice if I did not come home.

Hope you have a wonderful trip. My favorite tour book by the way is Rick Steves guide book. It is small, easy to carry and filled with excellent information.