Ideally a range hood would be vented to the outside. You can however get recirculating ones that have filters and blow the air back into the room. Bunnings do Bellini 60cm Recirculating Slideout Rangehood for $183. We had to put one in a kitchen that had the stove on an internal wall.
The model we used was a cheap slimline from Bunnings. It has the filters at the bottom, drop outs easily to clean. The outlet was either depending on which you capped at the top back if you have a shallow top cupboard with venting tube to top of cupboard or in our case I used the second option which was through flutes at the top front in the part that sits in front of the cupboard.
While not as good as a vented especially when smoking out the place my daughter has found it effective. More expensive ones do have replaceable carbon filters as well as the normal filters that catch the fat, etc. They do require more regular cleaning of filters to work at maximum efficiency. - JDE
You can get recirculating rangehoods and I recommend adding the charcoal filter which you can buy separately. - Stuardo
Here are some of the recirculating rangehoods available: