Since I am currently living in a hotel, I'm sharing my WiFi with a lot of other people. Some of them have an Apple TV or speakers that connect to WiFi. Ever since iOS7 my iPhone started connecting automaticly to some of them if there wasn't a password. I wasn't able to turn airplay off or on so I could use the speakers on my iPhone itself. Not owning an Apple TV myself made it quite annoying not being able to hear the sound of my phone.
However, by plugging in a headphone jack, opening Airplay (swiping up) and selecting it, then by plugging it out, the symbol of iPhone speakers returned and I was able to disconnect from other Apple TV's and speakers.
Hope this helps!
I've had this problem ever since I was at my friend's house- she has Apple TV- and my iPad connected automatically. So, I have no idea why any of the practical solutions that people think of are not options BUT, in terms of just getting it done, I did figure out a way. The key for me was getting near another Apple TV. I was out of town so I took my iPad to another friend's house who also has TV. Once I was logged onto their wireless network (the same network that their Apple TV is on-- that's how it connected in the first place), then the Airplay icon and options showed up from the bottom-draw menu and I was able to make sure that mirroring was turned off from the Apple TV section and to make sure the selection was on iPad instead. Problem solved. Now whether or not this will stay the same (rather than me having to make sure it stays at this setting everytime I link up to a network that has an Apple TV on it) I don't know. So my advice is find someone with Apple TV and connect to their network with your iPad and then change it.