The path to the backups should be ~/Library/Application Support/MobileSync.
You will not find your text messages there in a readable form. Apple intends that you use the backups solely to perform a complete restore onto an iOS device.
Well, I say "complete". Apple's use of the word "backup" here isn't what you might treat it as - it doesn't include your iOS install (so you can't use it to downgrade back to whatever version you were using before), nor does it include your actual apps (so they need to be present separately in your iTunes library when you attempt to restore). The backups more or less only cover your "personal" data.
If all you want to know is whether a backup was performed, load up iTunes, goto the iTunes menu up the top left of your screen, and enter Preferences. The Devices tab will list out your backup collection.
If you actually want to pick out individual bits of data from the backups themselves (eg your text messages), that's when you'd need to install a third-party program specifically for the task.