Recover iPhone backup manually from iCloud
Unfortunately, you are very limited in what you can do with that backup. In fact, there is literally nothing you can do with an iCloud backup unless you restore the backup. This can be done, however, on any iOS device (as in iPhone, iPod, or iPad), that is at least the iOS version that the stolen device was on. For example, if the iPhone 4 was running iOS 6, you will only be able to restore to a iOS 6, or 6.1 device.

If you are on a Mac, you should have easy access to Calendars, Contacts, Notes, Reminders, and such data. If you are on a PC, you can access most of that by going to iCloud.com. This isn't really the data that you've backed up, though, and it's really data that is just "synced" through iCloud. Either way, Contacts, are typically pretty important. 

If you own a Mac, you should be able to get your Photostream pictures by installing and opening Photostream. This doesn't capture videos, though. 

If you do have an eligible iOS device that you can do a restore on, be sure to back up that device locally before wiping. It might also be advisable to make sure that device doesn't do a backup of the newly erased setup to iCloud. If you keep that iCloud account disabled on that device, you should have an easy restore from iCloud, and a backup in iTunes should something go wrong.