I dumped a shop from my customer and imported it to my local system, as you can guess, the local domain is another one. All my domains are like: <customer>.dev.
Where to change domains
Secure/Unsecure Base URL
From core_config_data:
default 0 web/unsecure/base_url http://customer.dev/
default 0 web/secure/base_url http://customer.dev/
Check the skin/media/js url although!
default 0 web/unsecure/base_link_url {{unsecure_base_url}}
default 0 web/unsecure/base_skin_url {{unsecure_base_url}}skin/
default 0 web/unsecure/base_media_url {{unsecure_base_url}}media/
default 0 web/unsecure/base_js_url {{unsecure_base_url}}js/
default 0 web/secure/base_link_url {{secure_base_url}}
default 0 web/secure/base_skin_url {{secure_base_url}}skin/
default 0 web/secure/base_media_url {{secure_base_url}}media/
default 0 web/secure/base_js_url {{secure_base_url}}js/
Cookies
For cookies you should add the domain and the path, to secure your cookie. In your development environment, you can just use these settings:
default 0 web/cookie/cookie_path NULL
default 0 web/cookie/cookie_domain NULL