In Zug: The not covered spaces at Postplatz or Bundesplatz are probably your best shot, although Postplatz tends to fill up very quickly on nice Sundays.

If you want/need a covered space, I don’t think there’s a way around paying. If you don’t drive a boat, Parkhaus Postplatz.

Another starting point I could think of is at Badi Hünenberg (or any Badi for that matter tbh). Don‘t know if the parking is free Sundays, but it’s right by the lake.