Whenever we have to query multiple objects like in your case you need to query Case and Case comments prefer SOSL to query efficiently.

There is already a great reference to understand the difference between soql and sosl in below 
link  [when to use SOSL and SOQL][1]

So a SOSL on the case and case comments will be needed .

>Let me run through a how to use developer console for SOSL.Great news is we can use developer console of  for writing the  SOSL query 

Here is the sample query.Please modify as you needed 

   > **FIND {hello*} IN ALL FIELDS RETURNING case(Id,CaseNumber),casecomment(ParentId,CommentBody,Parent.CaseNumber)**

The screenshot of how the result looks like

![enter image description here][2]


  [1]: http://salesforce.stackexchange.com/questions/9028/soql-vs-sosl-which-one-to-use-and-when
  [2]: http://i.stack.imgur.com/TN63w.jpg

UPDATE:

This is how the query will include where clause
 

    FIND {hello*} IN ALL FIELDS RETURNING case(Id,CaseNumber where createddate<TODAY),casecomment(ParentId,CommentBody,Parent.CaseNumber where ParentID!=null)