I always run queries in phpmyadmin http://www.phpmyadmin.net or adminer http://www.adminer.org/:
UPDATE wp_options SET option_value = replace(option_value, 'http://www.olddomain.com/', 'http://www.newdomain.com/') WHERE option_name="home" OR option_name="siteurl";
UPDATE wp_posts SET guid = replace(guid, 'http://www.olddomain.com/','http://www.newdomain.com/');
UPDATE wp_posts SET post_content = replace(post_content, 'http://www.olddomain.com/', 'http://www.newdomain.com/');
Yes, some will say to never change the GUID, but changing the domain gives you no choice. Your posts will show up again in RSS feeds.
Use phpmyadmin or adminer; dumping the database and doing a find/replace with a text editor will break serialized data.
After those queries, do a simple search for the IP to find other instances in options, meta and other tables, etc.
You may find instances of the IP in widget serialized data in the meta and options tables, but change those values in the widget itself, because such serialized data must be the same length or it will break. Or use a find/replace tool at http://interconnectit.com/products/search-and-replace-for-wordpress-databases/ that re-serializes data correctly and can also find/replace all URLs without using the above queries separately.