Passing a literal ? to sp_MSforeachdb
Updates thanks to Martin. If you view the text for the procedure:

EXEC sys.sp_helptext N'sp_MSforeachdb';


You will see that it passes the @replacechar as NCHAR(1) (default N'?') into sys.sp_MSforeach_worker. Peeling back another layer of the onion, you will see really ugly code in that procedure that loops through every character in the command and rebuilds it. I didn't study every single line but I could not find any evidence of an ability to escape or preserve the actual question mark conditionally, unless - as Martin points out - you override it with a different character that can't naturally appear in the command. So perhaps something like:

EXEC sp_MSforeachdb N'SELECT ''Ƥ'', other_columns FROM [?].dbo.whatever
  WHERE DirectoryPath LIKE ''%?%'';', N'Ƥ';

-- Ƥ is NCHAR(420), chosen randomly


Since it is really looking for the literal ? character, a possibly easier way would be this:

EXEC sys.sp_MSforeachdb N'PRINT ''?'' + ''-'' +  CONVERT(VARCHAR(32), 0x3F)';


So extrapolating that, we can construct this ugly variation:

EXEC sys.sp_MSforeachdb N'SELECT ''?'', other_columns FROM [?].dbo.whatever
  WHERE DirectoryPath LIKE ''%'' + CONVERT(VARCHAR(32), 0x3F) + ''%'';';


That all said, you could write your own version of sp_MSforeachdb that uses a different default value for @replacechar, so you don't have to override it manually. You probably should be writing your own version instead of relying on the built-in procedure anyway, as I point out in these posts - it is unsupported, undocumented, and actually has a very high frequency bug where it skips databases due to the cursor options used:


https://sqlblog.org/2010/12/29/a-more-reliable-and-more-flexible-sp_msforeachdb
https://sqlblog.org/2010/02/08/bad-habits-to-kick-relying-on-undocumented-behavior
http://www.mssqltips.com/sqlservertip/2201/making-a-more-reliable-and-flexible-spmsforeachdb/