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.
From Apple's Photo Stream FAQ:
How long are My Photo Stream photos stored in iCloud?
The photos you upload to My Photo Stream are stored in iCloud for 30 days to give your devices plenty of time to connect and download them.
How many photos are stored in My Photo Stream on my devices and computers?
iCloud pushes all your photos to the My Photo Stream album on your devices and computers, and manages them efficiently, so you don’t run out of storage space.
Your iOS devices keep a rolling collection of your last 1000 photos in the My Photo Stream album. From there, you can browse your recent photos or move the ones you like to your Camera Roll or another album to keep them on your device forever.
So, you'll have to sync them in from iPhoto using iTunes, since Apple only keeps your photos for 30 days on their servers.
You could also find another app on the App Store like Documents by Readdle and copy the photos onto your phone over Wi-Fi (bypassing iTunes as you wanted) but I realize that's less than ideal.
Best Answer
If you have a copy of the backup, there are a couple of ways to get these back.
Free http://www.itunesextractor.com/extract-photos-from-iphone-backup.html
Paid https://www.imobie.com/phonerescue/
I would make a backup of your file, then try the free one first and if that doesn't work try the paid version if these photos are important.
Hope one of these will work!