if value exists

here is one way

I have replaced the

Sub TodaysDate()
   Dim rFound As Range
   Dim lLR As Long
   
   lLR = Sheets("Closed Cases").Cells(Rows.Count, "b").End(xlUp).Row
   
   Set rFound = Sheets("Closed Cases").Range("b2:b" & lLR). _
      Find(what:=Date, SearchOrder:=xlByRows, SearchDirection:=xlPrevious)
   If rFound Is Nothing Then
      Sheets("Closed Cases").Cells(lLR + 1, "b").Value = Date
   End If
   Set rFound = Nothing
End Sub

Please note that you should avoid using macro & variables names that match commands used by Excel & VBA. e.g. Today, Rows, Sheets etc
Using such names can cause unexpected results

For Your Info
Most times you do not need to select sheets, cells etc to work with them
Macros actually run faster & can be easier on the eyses if you do not select or activate sheets etc

The code you posted could be replaced by a single line command

Sheets("Closed Cases").Cells(Rows.Count, "b").End(xlUp).Offset(1).Value = Date