I went to many shows alone during my tour in Germany from 1988 -1990.
Most memorable trip was travelling over 300km to see Manowar headline a Metalfest at the Phillipeshalle in Dusseldorf. Fates Warning, Sabbat, Lizzy Borden, Saxon, and Manowar. It was a night I'll never forget.
Next would be travelling to Nuremburg to see Overkill and Mordred. Ended up spending the entire day hanging out with the road crew. Got to meet the guys from both bands and got to sit in during Overkill's sound check, and then topped it all off by watching the entire show from the mixing booth. All because I spoke English, haha.
So, yeah, going to see a show alone can be a blast, it can even be one of those events that you never ever forget.