I'm inclined to think of it as cities because of the similarity with the Dutch word stad, but I think it actually seems to mean place in the general sense, which could be anything ranging from a spot on a seat to a solar system or whatever.
"Old English stede meant ‘place’. From a Germanic source, it is related to Dutch stad ‘town’, German Statt ‘place’, from an Indo-European root shared by the verb stand. 'Instead' (Middle English) is simply ‘in stead, in place of’ run together. The adjective steadfast [Old English] is literally ‘standing firm’; a homestead (Old English) is your ‘home place’; while if you are steady (Middle English) you are not easily moved from your place." -- Oxford Dictionary. I do love a bit of etymology... good catch there LucBE! ;)
I’d like to add here that nowadays in Germany nobody would say "Statt" for place (except for lawyers). The modern German translation for the Danish word "Sted" is "Stelle" what sounds pretty similar.
Just looked this up in the OED: 'stead' is the same in Old Norse and in Old Frisian, making it a Norse/Saxon inheritance.