I'd probably choose
Adriana, but I like
Adrienne as well. I don't think it's dated at all, but then again I've never known any. I pronounce it ay-dree-EN, with slight emphasis on the last syllable. It's different than the way I pronounce the male form,
Adrian: "AY-dree-en", less emphasis on the last syllable makes the name feel more masculine to me.
Have you ever considered
Adria?