Suggesting Reviewers: How to find institutional affiliations
How do you know of these potential reviewers in the first place?

If you know them personally, then you probably also know which institution they're in. If you don't know them personally but have read their papers which are intimately related to yours, then you can look at the first page of their papers to see their affiliation. If you read of them from books, you can still look at the title pages which should list their affiliation.

If they don't have affiliations, then simply write "unaffiliated".