I think it varies on the cat in terms of how long it takes them to recover. Some seem fine the next morning, while others take a few more days for activity/personality to return to normal. My little girl was spayed yesterday, and she's doing just great.
However, even if a cat seems fine fairly soon, one still has to be around for about 10-14 days in order to check the incision daily. You have to be able to make sure there is no discharge/puss (infection indication), bleeding, or missing stitches. The above can be caused from excessive licking/biting or a high activity level which can include jumping a lot etc. and must be prevented should it occur. You also want to make sure that her appetite (among other things) in normal during that time period. Like another poster said, you might also want to confine her to a smaller space where jumping and running around can be kept to a minimal.
Your vet will probably explain more of the above in detail when she is discharged.
I hope I'm not scaring you as Spay/neuter recoveries are generally quite straight forward without incident. However, an owner's presence during that time is still very important incase any complications do happen to arise.
Good luck and I'm sure your girl will make out just fine.