Bremer Ratskeller at lunchtime is definitely an "any-clothes" venue.
The one I don't really know myself is "Alt-Helgoländer Fischerstuben" in Hamburg, and we're going there in the evening, but does any of us really want to carry about a second set of clothes for the entire day???
So for the Hamburg-day you might want to get dressed in something OTHER than your Iron Maiden t-shirt and sawn-off jeans in the morning already...
"Portofino" in Fintel is so very much an "anything-goes" restaurant, and just in case (and I sooooooooooooooooo hope it will be the case!) the good weather we're having just now will not have exhausted itself by the last week of May, they'll seat us outside, anyway.