You might save some money for registering a domain name with a hosting company, but I would take into consideration the reliability of a hosting company and the price. It is more important to look at the cost of the hosting because you pay that every month, versus the domain name every year.
My choice for web hosting is HostGator. Cost for the domain with them is $15, but their web hosting service is one of the best out there. and the monthly cost starts from $4.95. You can save close to $10 if you use coupon code: HOST994HGH
If you want to save on the domain name register it with GoDaddy and use a coupon there as well. For example coupon code CJC749NOT will save you a few bucks: you will be able to register a domain name for $7.49. They also offer hosting but I would not recommend that. Hosting at GoDaddy is not that great.