There are lots of domain selection tools available online which allow you to search your desire domain name quickly and check the availability of your domain name. For example, Domainr finds domain names and short URLs and instantly check availability and register for all top-level domains, Dot-o-mator to create domain name suggestions, BustName lets you enter words and it will try every combination and tell you which are available, and many more.
In case you only want to check the availability of domain name quickly, I suggest you to use ajax domain selection tools AJAXWhois and Domjax as they make it exceptionally easy to determine availability of a domain name. Normally if I want to create a new domain name, normally I will use this two domain selection tools to help me search for the best domain name that I like. If you never heard them before, check out their site, I believe that you will like them.