The Brita is a great idea - the Vegas tap water tastes really metallic and you'll want to drink a lot of water.
Check out this site, they have some great tips on some cheaper stuff to eat and do. It's not really kid friendly, but some of the things will be good for your kid.
Cheapo Vegas - Your Guide to a Better Vegas Vacation
Linked off that site and by the same guys, here's a good list of the free stuff to look at:
Free Stuff to See - Big Empire - Las Vegas on 25 Cents a Day
You don't mention where you're staying. There may not be a coffee pot in the room.
There are cheaper (and nice) places to eat all over the place if you look for them. I love the Main Street Station casino that's downtown, they have a brew-pub that has some good happy hour specials M-F, I think it's 4-6pm. A few appetizers from there make a pretty good light meal, and follow it with an ice cream from Lapperts (great hawaiian ice cream) at the Californian next door. Main Street Station also has a steak house that I enjoy that's reasonably priced, and they have incredible antiques (including a piece of the Berlin Wall in the men's room). While most downtown casino's aren't great for kids, you'll be fine there. Hit one of the overhead shows on Fremont, and you've got a great evening.
One of the most fun cheap things I did in Vegas was check out the Pinball Hall of Fame museum. Las Vegas Pinball Hall of Fame Pinball Museum, Nevada NV, Tim Arnold
The AC wasn't very strong, but the games were cheap to play, and worth the drive over there if you have a car.