Niederegger is the institution. The ground floor is the shop — every conceivable shape of marzipan, dark-chocolate-coated bars, marzipan pigs, marzipan models of the Holstentor. The café on the first floor serves the famous Nusstorte with whipped cream, hot chocolate, and the Lübecker Cocktail (marzipan ice cream and a shot of strong coffee).
The upstairs Marzipan-Salon, free to visit, holds a small museum with the life-sized figures and a history of the trade. Touristy, of course — but unavoidable, and the cakes really are excellent. Open all day; queues at peak holiday times.