I need to be able to move wordpress sites to new domains. This is not really for SEO purposes just for something else that I'm doing.

I'm familiar with moving my wordpress files to a new host, and importing the database. I do this all the time manually with no problems.

But I've been searching and posting everywhere in forums and can't find the answer to this simple question.

Is there a way to move your wordpress site onto a new domain and have it appear exactly as the old site, but with all of the images hosted on the new domain, and links to inner pages on the new domain? (Also: have your domain.com/wp-admin link take you to login to the new site, not the old one)

In the past I have moved some sites to new domains but I always have problems that I can't completely fix- the image URLs are still hosted on the old domain, all of the inner page links are pointing to the old domain, the wp-admin login points to the old domain, etc.

I've seen people say "just buy BackupBuddy" and I am definitely willing to buy something to help me do this quickly on a lot of sites, but i just don't see what backup buddy actually does for this particular purpose- it basically just downloads your database and wordpress files, as you can do manually. One thing I have tried is going through the database file and replacing the old domain name with the new one and then uploading the database file to the new site- but that doesn't really work for some reason and still doesn't do what I want. I think getting the images to be hosted on the new site may be the hardest part of this.

I'm sure somebody knows the answer to this.