I am guessing you are concerned about someone taking issue with a CD. Probably won't happen. I've done this a bunch of times with a girlfriend. It took me a while to learn to dress appropriately for the venue. All the places you mention, it is normal for a woman to be in jeans, boots and sweater this time of year. I am guessing you see yourself something more feminine, it will attract more notice but I still doubt any scene will be made. I say go for it, I've never had the slightest issue. Servers want tips, friendly ones do better in that line of work. That's what you will probably get so treat him it her nicely. Enjoy.
BTW. Movies are great for first forays into enfemme dates with SO.