Getting database sizes on an MSSQL Server named instance
If you just need the size of the entire database then below script will help you :

SELECT  @@servername as server_name,
        d.name,
        CONVERT(DECIMAL(10,2),(SUM(size * 8.00) / 1024.00)) Size_MBs
FROM    sys.master_files mf
        INNER JOIN sys.databases d ON d.database_id = mf.database_id
WHERE   d.database_id &gt; 4 -- Skip system databases
AND     d.state_desc = 'ONLINE'-- ONLY get size for ONLINE database.
GROUP BY d.name
ORDER BY d.name


If you want to automate your migration of databases from one server to another, I highly recommend using sqlmigration - a powershell script that will migrate your databases, jobs, logins, etc from one server to another. Also, be aware of the pre and post migration steps if you are moving from one version of sql server to higher (2012 or 2014) version.

Depending on your size of databases and the amount of downtime, there are ways that you can implement to minimize the downtime for your entire migration - e.g. using logshipping or mirroring and then during cutover, just failover to the new server, etc.

Always prepare and test your migration and rollback procedures.

Edit: From your screenshot, it seems that you do not have permissions. Can you just do a select * from sys.master_files