The best database for finding local or national competitors is Reference USA. When you enter the database, click on US Businesses and in the next screen, click on advanced search. You will then be able to use the facets on the left side of the page to identify the type of businesses you are looking for. The most useful combination is Industry Type and Geography. Use the NAICS code if you know it from your industry research, or use keywords for either SIC or NAICS codes in the selection box. Define the geography by what is appropriate for your market. You can download any results into excel spreadsheets and create maps. Reference USA will give you a family tree link to assemble a whole company, and it gives size estimates for individual locations (sales, square feet, number of employees) which can give you a reasonableness check on what performance levels are possible.
The other place to find breakdowns of numbers of enterprises by state or country is Business Source Complete. Go back to the industry research tab for instructions.
If you can identify a smaller or privately held company in the same field, you can look them up in Hoovers, which contains brief profiles of many companies and each report contains a list of competitors,