Give it to the person. They'll really appreciate it. It's fantastic when they share their music back. I hope that this Instructable helped, now go out...
Mix CDs are great gifts that show that you put some effort into the gift. But if you just throw together a playlist, it comes off as sloppy, lazy, and unimaginative. In this instructable, I'm going to give you some tips for making a mix CD.
Go through your iTunes (or however you store your music) library, and pick out songs you like. Pick out some songs that you don't like as much, too. They may not be the best, but if they go together, it will sound good. Don't think about the person, just throw some songs together that might go together.
Step 2: Refine the music
Go to the playlist, and look through the songs. If you have a bunch of stuff by one artist, try to narrow it down to no more than two. Pick a good hook. I like to use "For Your Own Safety!" by the Aquabats, because it's fun, funny, and draws you in. Switch around the orders to something that might sound good. Then, listen to the beginning and end of each song, to see if it transitions well.
Step 3: Consider your audience
Think about who you're giving this to. If it's to a close friend, don't worry about the song. Try to use music that the person doesn't already listen to, but not something that they wouldn't listen to. If I'm giving it to someone who I don't know well or with which I have a formal relationship, I look at the lyrics for all of the songs. If the song contains something that you wouldn't say in front of them, consider leaving it out. It may be a bit paranoid, but it reduces the chances of the CD causing some awkward situations.