There are lots of tools out there that can help you find and pick a domain name. These tools would probably not be necessary if any domain name were available. But lets be realistic as most ideal domain name choices are likely already taken.

Sometimes a domain name registrar itself (ie Network Solutions or GoDaddy.com) may provide alternative available domain choices if your domain search resulted in an unavailable domain name. However, oftentimes the choices provided by registrars are not that great or may not relate as closely as you'd like to the initial domain choice.

A tool and website I use and recommend is DomainTools.com which offers a Domain Suggestions tool that makes various suggestions of available domain names given your original search criteria. DomainTools.com offers this service as well as many other web domain name tools, some of these services for free and some for a fee.