In the modern era, is it still against to set an alarm so that one wakes to music? Does it make a difference if it is a radio station or a cd?
The question doesn’t specify when: On Shabbos, or during the week.
During the week, there is no problem with waking up with music.
On Shabbos, one should not wake up with radio and music, for two reasons.
One, which is maris ayin (it looks like the radio was turned on on Shabbos) can be overcome by ensuring that the volume is not sufficient to be heard outside the room (see Iggros Moshe 4:70).
Note that although alarm clocks are common today (lessening the concern for maris ayin with a regular clock), it is not necessarily common to wake up to music, and the concern might still be in place.
But in addition, it is not in the spirit of Shabbos to listen to music and the radio on Shabbos.
Therefore, for Shabbos a regular alarm clock should be used.