The previous code had a possible problem, namely that if today is Saturday, it gives today's date. If you do not want that to happen, the following avoids that, and can be adjusted for any day of the week.
@echo off
setlocal enabledelayedexpansion
>evaluate.vbs echo Wscript.echo eval(WScript.Arguments(0))
set VBcmd=cscript //nologo evaluate.vbs
set NDW=Saturday
For /L %%A in (1,1,7) do for /f "delims=" %%N in ('%VBcmd% "weekdayname(weekday(date+%%A))"') do if "%%N"=="%NDW%" set Offset=%%A
for /f "delims=" %%Y in (' %VBcmd% "year(date+%Offset%)" ') do set yyyy=%%Y
for /f "delims=" %%M in (' %VBcmd% "month(date+%Offset%)" ') do set mm=%%M
for /f "delims=" %%D in (' %VBcmd% "day(date+%Offset%)" ') do set dd=%%D
if %mm% LSS 10 set mm=0%mm%
if %dd% LSS 10 set dd=0%dd%
del evaluate.vbs
echo Next %NDW% is %yyyy%%mm%%dd%
pause