1. My Visa Jobs
Here is the website I referred to find who actually sponsored international students/workers.
You can search by job title, company name, state, etc. You can also see some immigration document that was processed
Here is another website with similar information that I recently found. It seems to have better user interface overall.
Keep in mind that bigger company will naturally have bigger numbers. Also try to consider %.
OTs, you may notice that there are more rehab companies that sponsored for H1b or green card than any other type of organization.
It’s also helpful that the websites give you some idea about salary range that is specific to international employees.