The Villa Esche is a 1903 Jugendstil villa designed by Henry van de Velde for industrialist Herbert Eugen Esche — one of the finest examples of van de Velde's domestic architecture in Germany, and worth seeing. The café in the grounds serves lunches, cakes, and coffee in a setting that beats most of what the city centre offers.
It's a slightly out-of-the-way destination — the villa is in the southern Gablenz district — but the combination of architecture and a decent meal makes it worth the tram ride. The café keeps gallery hours rather than restaurant hours; check before going specifically for dinner.