Stay at the hospital. Some hospitals will allow the spouse to stay and may even have an extra bed in the maternity ward rooms for that purpose. See if your hospital is one of them and make use of it. Be warned, you might not get much sleep, though, between the low comfort level of most of such beds, and the night feedings and health checks.
Have a friend or three over. Think of it as another bachelor party. It's your last night/few nights of "freedom" before starting a new chapter of your life where someone else is dependent on you. You can also celebrate being a dad. Have a beer, smoke a cigar, have a Halo LAN party marathon, or whatever you do with your friends for fun. They can also help you get some of the other stuff done, too, especially if you still have a lot left.
Make a baby blanket. This one's a little off the wall, but I can't resist. Take up sewing, knitting, or crochet and make a simple baby blanket. If you have a few hours each day, you could knock it out within a week. It may not look like your grandma's blankets, but your baby won't care, and you made something. (Additionally, it doesn't have to be of this sort, if you have the woodworking materials, you could always make something that way, or whatever else suits your fancy. Knitting and crochet just happen to have fairly low barriers to entry.)
Train your dogs. If you have pets, you should be training them to be familiar with the baby, before baby ever even comes home. Up until now, you should be getting them familiar with the baby stuff. Now that baby's born, you should take home one of the blankets baby used, so they can get used to the smell. Give them lots of attention and love while exposing them to the baby's scent so they won't freak out at much when baby comes home, and to help curb jealousy.
Go grocery shopping. When was the last time you actually went shopping? Between Mom having no room to each much, and everyone's anticipation of the baby coming (and maybe even the excitement/anxiety of being in the hospital for a week), you're probably light in the food department. Also, now will be the time to determine whether you'll need formula and would be a good time to pick that up if you do. The same goes for diapers. Get that stuff and be ready to play chef. You can even cook up some meals ahead of time so you don't have to worry about it in the first couple of days that baby's home.
Go shopping for Mom. She's probably going to be feeling pretty "blargh" about now, between being worn out with baby, coming down from the high of the pregnancy and birth, and dealing with things like postpartum depression, C-Section scars, or extra weight she may have gained while pregnant. If you can, find out what her size is now, and go pick up something sexy (or at least nice looking), or something else that you know will make her feel good about herself.
Finish the nursery. Even if it's "finished" in the sense that it's ready for baby to move in, see if there's some final polish you can add to it. Hang pictures, touch up the paint, make sure the changing station is ready, dust, polish, etc.
Clean up the house. Like the shopping, some things may have been neglected. Now's the time to catch that stuff up, so you're not trying to do it around a newborn's "schedule". It's also nice to come home to a clean house. Don't forget to pay the bills, too.