Using the technique I discussed in this post, the following SQL Server stored procedure can be used to display the number of rows in each table and used/unused space for all tables in a specified database. Put the stored procedure into whatever database you use for your Utilities database, then run the procedure from anywhere, passing in the name of the database for which to display row counts.
Note: The contents of the “@sql” SQL Query used inside this stored procedure is from the StackOverflow.com answer by “marc_s” on Oct 25 ’11 (edited Oct 29 ’13) to the question “Get size of all tables in database“. My contribution was simply to turn that query into a stored procedure that could access any database and to add the “Grand Total” values.