Lost Odyssey is very very good, and feels very FF7 esque if you take the fact it's a very tried and true JRPG, and is quite a long game at 4 discs (which it's worth installing on the 360 as it cuts load times by about 1/3).
Star Ocean is also good but has one of the most annoying characters known to man...'kay? That said the graphics and general multiple sub plots of the game make it worth a shot.
Eternal Sonata is utterly charming, and actually really rather good, so I'd definately recommend it if you like asian influenced titles; it also has an almost unreal amount of respect for Chopin, and is a slightly touching game, with an equally bizzarre ending.
If you're after a more EU/US RPG, then Mass Effect and Fallout are both worth a play; Oblivion also however I always found it a little too open world to get into.
Enchanted Arms if you can find it is a reasonably well made little JRPG that can be had very cheaply, and looks pretty good, however is a little basic (probably a 7/10 game, reasonable, but not special)
Blue Dragon is a true JRPG, looking like an Anime, has some annoying characters but is moderately solid.
I haven't played Tales of Vesperia yet.
My personal picks as best on the console would be Star Ocean 4, Mass Effect and Lost Oddysey, with Fallout 3 and Eternal Sonata narrowly missing out. All are worth installing onto your HDD though, as they all benefit to a greater or lesser extent.
I haven't got round to playing Infinite Undiscover or Last Remnant either, but I understand both are fun but flawed; Lost Oddysey or Star Ocean 4 are a better example of the genre, in slightly different ways.
As a run-down, out of 20, I'd give the games:
Star Ocean -17
Mass Effect - 18
Fallout 3 - 16
Oblivion - 15
Eternal Sonata -17
Lost Odyssey - 18
Blue Dragon - 15
Enchanted Arms - 14