If the cursor is at the start of a cell with multiple lines then as you have discovered the Down Arrow will move to the next row. The range of shortcuts for Word tables is:
TAB Next cell in a row
SHIFT+TAB Previous cell in a row
ALT+HOME First cell in a row
ALT+END Last cell in a row
ALT+PAGE UP First cell in a column
ALT+PAGE DOWN Last cell in a column
UP ARROW Previous row
DOWN ARROW Next row
You could always assign a keyboard shortcut to a macro e.g.
Code:
Sub MoveDownARow()
Dim oRng As Range
If Selection.Information(wdWithInTable) Then
Set oRng = Selection.Cells(1).Range
oRng.End = oRng.End - 1
oRng.Collapse wdCollapseEnd
oRng.Select
Selection.MoveDown Unit:=wdLine, Count:=1
End If
End Sub
http://www.gmayor.com/installing_macro.htm