VBSEdit program installs a COM library VBSEdit Toolkit, which allows Open File dialogs.
From VBSEdit help:
Dialog boxes 
OpenFileDialog method
Prompt the user to open a file
toolkit.OpenFileDialog ([initialFolder,[filters,[multiselect,[title]]]]) 
'Opens a single file
Set toolkit = CreateObject("VbsEdit.Toolkit")
files=toolkit.OpenFileDialog("c:\scripts\","Text Files (*.txt)|*.txt",False,"Open a text file")
If UBound(files)>=0 Then
  WScript.Echo files(0)
Else
  Wscript.Quit
End If
'Opens multiple files
Set toolkit = CreateObject("VbsEdit.Toolkit")
files=toolkit.OpenFileDialog("c:\scripts\","Text Files (*.txt)|*.txt",True,"Open a text file")
If UBound(files)>=0 Then
  For Each filepath In files
    WScript.Echo filepath
  Next
Else
  Wscript.Quit
End If
SaveFileDialog method
Prompt the user to save a file
toolkit.SaveFileDialog ([initialFolder,[initialFilename,[filters,[title]]]]) 
Set toolkit = CreateObject("VbsEdit.Toolkit")
filepath = toolkit.SaveFileDialog("c:\scripts","test.txt","Text Files (*.txt)|*.txt")
If Not(IsNull(filepath)) Then
  Set objFSO = CreateObject("Scripting.FileSystemObject")
  Set objFile = objFSO.CreateTextFile(filepath,True)
  objFile.WriteLine Date
  objFile.Close
Else
  Wscript.Quit
End If
SelectFolder method
Prompt the user to select a folder
toolkit.SelectFolder ([initialDir,[title]]) 
Set toolkit = CreateObject("VbsEdit.Toolkit")
myfolder=toolkit.SelectFolder("c:\scripts\","Please select a folder")
If Not(IsNull(myfolder)) Then
  WScript.Echo myfolder
Else
  Wscript.Quit
End If
…
(Actually, folder selection dialogs can be opened without VBSEdit toolkit, with BrowseForFolder method of Shell.Application object.)