I was going to say I wouldn't have a problem driving into the city with Friend as long as she met me at my house and provided her own transportation to and from my house. However, it occurred to me she could find a problem with getting to my house and make it so that I'd have to pick her up after all so I'd go with meet her at the venue. I'd also prepare to be attending the concert alone in case it comes to that (if you've never attended alone, it is weird at first, but you get used to it if you determine that you really don't care that you're attending alone -- I started doing it years ago when I found there were lots of things I wanted to do for which I couldn't find someone to accompany me).
If the concert should be that important to your friend, she will figure out how to get to/from the city on her own (and if she manages to get to the venue without driving and needs a ride from the venue, be braced to tell her that you can't drive her home, can drop her off at the nearest public transportation on your way home for her to get home or you could drive back to your house with her and she could catch a cab or something home from there).
And, there's one more option -- you call her on it and say, "Look, I'm not available to hang out all weekend. If you want me to do all the driving, then you need to pay for all the gasoline between my house and yours and for the parking (all the parking because I'm doing the driving and it's my car getting all the wear-and-tear). If that's not okay, then we'll just meet at the venue.