想改個日文名..

You are picky.
簡單、可愛、 易記？ These are very subjective factors, I can't really decide for you.
Anyway, I'll try to point you to the right resources. Go to this page:
http://www.dd.iij4u.or.jp/~ume20/f_name/
And download the data file for reference
http://www.dd.iij4u.or.jp/~ume20/f_name/f_name20080506.zip
I manage to pull off these entries from the list, based on your first two criteria:
Mai 舞雪
Maki 天雪
Mayu 真雪、舞雪
Miyu 深雪、美雪
Moyu 桃雪
If you want three syllables, here are your options:
Maiyu 舞雪
Mayuka 舞雪香
Mayuki 真雪、舞雪、舞雪季、麻雪、苺雪
Mayuko 舞雪子
Mayumi 雅雪実、舞雪美
Mizuki 瑞雪
Miyuki 海雪、希雪、見雪、光雪、三雪、実雪、心雪、深雪、深雪樹、瑞雪、聖雪、雪雪、美雪、美雪季、文雪、碧雪、峰雪、未雪、魅雪、蜜雪、弥雪
Meyuki 芽雪
Moyuki 萌雪
I personally don't know how many of these forenames actually exist, but I believe many of them do.
Anyway, hope that helps.

Miyuki　美雪／美由紀