There are definitely a lot of difficulties associated with venting an island here are some options
1- use a high efficiency hood with charcoal filters -- for most cooking needs this is sufficient
2- if this is not enough, use this combined with a vent fan on an outside wall.
3- Go to church and pray that your joists run towards the direction of the outside wall
4- rum the vent along the ceiling and box it in
I would shy away from down draft venting-- it dosen't tend to be as efficient as upward vents
For more kitchen ideas, visit LongIslandKitchenAndBath.com
Well... you need a contractor to see whether you can place an island hood or a down draft vent. Hopefully, you do not have any obstructions such as a beam in the ceiling, or it may be too far from the exit point, or maybe you have a second story. I am assuming you did not use a contractor for your remodel, which is why you've forgotten the hood. So find one now, and he will take you thru the motions regarding your options. Good Luck!