There are many think tanks (research organizations) and NGOs (non-governmental organizations) that produce research and statistics on immigration. While many are non-partisan, they often have a specific mission or policy focus that you'll want to keep in mind as you read their publications.

Databases:

Search across reports from many different organizations.
e.g.: try searching for "immigration" and [country or city]

Specific research organization websites:

Look for sections called "Research," "Publications," "Analysis" or try searching the site. Some can also be browsed by country.