Default Instance:

Install Path: HKLM\Software\Microsoft\MSSQLServer\Setup\SQLPath

If they are defined:

Default Data File Path: HKLM\Software\Microsoft\MSSQLServer\MSSQLServer\DefaultData

Default Log File Path: HKLM\Software\Microsoft\MSSQLServer\MSSQLServer\DefaultLog

Named Instance:

Install Path: HKLM\Software\Microsoft\Microsoft SQL Server\<Instance Name>\Setup\SQLPath

If they are defined:

Default Data File Path: HKLM\Software\Microsoft\Microsoft SQL Server\<Instance Name>MSSQLServer\DefaultData

Default Log File Path: HKLM\Software\Microsoft\Microsoft SQL Server\<Instance Name>\MSSQLServer\DefaultLog