Fonts for PolyTonic Greek

Fonts for PolyTonic Greek

I am using XeLaTeX with the fontspec package for Polytonic Greek character
support (Unicode solutions only, no hacks). The default font doesn't
display most of the desired characters, but I like the default font for
all of the Latin characters. What are some fonts that support the full
range of PolyTonic Greek characters (with diacritics) but also look
similar to the default font? The only font I know of that supports all the
characters is DejaVu Serif, which I don't like the look of at all.
I am also open to a solution that will automatically render Greek
characters in an alternate font but let me use the standard font for all
Latin characters. I'd be happy to do something like \greek{Âίâëïò
ãåíέóåùò Ἰçóïῦ ×ñéóôïῦ õἱïῦ
Äáõὶä õἱïῦ Ἀâñáάì.} as well if that puts it
into a different font that works (but please suggest fonts or help me find
a list).