Can I ask what places "seem intriguing" ?? I may be familiar with some of them. A few of the 'fancier' brunch buffets are still on hold because of Covid, so the options are more limited than normal. There is also the "city run" in Luzern this Sunday (12th Sept) and some places in old town will be closed because of the race, in case you're arriving this weekend.
For a unique venue with interesting views, there is a nice rustic brunch at the farm by the city walls from 930am-3pm on Sundays (online reservation possible). You can check out the Highland cattle and the walls after you enjoy your food! The farm has a page in German https://www.hinter-musegg.ch/hofbeiz (Hofzmorge is the name for the brunch, 45/person incl non-alcoholic drinks, lots of locally produced food) or you can google Kulturhof Musegg and look some photos.
Mill'feuille is also pretty popular with locals, relaxed cafe next to the river. They had to close for a little while after the flood this summer, but are open again. You can check their website for info. I think they have English menus there too and their 27chf breakfast option is a good deal. It can get busy if the weather is nice, but you can reserve online.