Using a cursor with a CTE

It is fine to use @ in a cursor name but the syntax you are using is wrong.

DECLARE @adate DATETIME
DECLARE @FROMDATE DATETIME
DECLARE @TODATE DATETIME

SELECT @FROMDATE = getdate()

SELECT @TODATE = getdate() + 7

DECLARE @weekdates CURSOR;

SET @weekdates = CURSOR FOR
WITH DATEINFO(DATES)
     AS (SELECT @FROMDATE
         UNION ALL
         SELECT DATES + 1
         FROM   DATEINFO
         WHERE  DATES < @TODATE)
SELECT *
FROM   DATEINFO
OPTION (MAXRECURSION 0) 

OPEN @weekdates

FETCH next FROM @weekdates INTO @adate

WHILE @@fetch_status = 0
  BEGIN
      PRINT 'success'

      FETCH next FROM @weekdates INTO @adate
  END

When declared as a local @ variable the cursor is automatically closed and deallocated when the variable goes out of scope.

Just put it in before the common table expression:

DECLARE @FROMDATE DATETIME 
DECLARE @TODATE DATETIME 
select @FROMDATE=getdate()
select @TODATE =getdate()+7

declare boris cursor for

WITH DATEINFO(DATES)
     AS (SELECT @FROMDATE
         UNION ALL
         SELECT DATES + 1
         FROM   DATEINFO
         WHERE  DATES < @TODATE)
SELECT *
FROM   DATEINFO
OPTION (MAXRECURSION 0) 

(However, insert usual cautions about cursors almost always being the wrong tool for the job. If you can find a way to do the whole operation in a set based manner, it's usually preferable, and likely to perform better (or at least be more amenable to performance tuning))