Can you be more specific on your budget?
Gibson Les Paul Studio with Catswhiskers pickups
PRS SE 'Floyd' Custom 24 with Creamery pickups
Fender Standard Stratocaster with DiMarzio pickups
Takamine GN30
BluGuitar AMP1
well a great working floyd bridge would be an original floyd and they cost around 200 all by themselves so there arent really any guitars like that. cheap guitars have cheap parts and theres really no way to get around the "you get what you pay for" thing. i would say ibanez has the nicest cheap guitars with a decent locking trem though. and you could always find a guitar you like that has a cheap-o floyd copy and just replace it with the real deal when it wears out or right away if its already not functioning right which might happen with a year of playing or right out of the box.
Gary Kramer Crusader
Ibanez S320
Used Ibanez Rg550

And the cheapest.

Both have the Floyd Rose Special Bridge which is essentially the same as an OFR but it is built in South East Asia and has a Zinc block and saddles. Google Floyd Rose special, they're decent trems.
Aliadiere - sadly has more syllables than goals this season."
Setanta commentator during Newcastle-Middlesbrough. .
Cort KX5FR is under £300 in UK. Anything much less will not have a nice FR. (Yes I know Swift do their Metal Axe for £59 but its a £5 trem on it.)
I pick up my guitar and play
Just like Yesterday

T C Ellis Series 2 LP w/Skatterbrane Quiescence pups
Cort EVL-K6
Yamaha RGX211 modded
H&S Electric 12-string
Shaftsbury Ricki 4001
'84 Fender Yale
Roland Cube 15x

Dude I think what you need is a Peavey Predator Plus EXP ($219 in Musician's Friend). They are pretty good quality for the money: