Visitors to the gallery – and to Riga in general – shouldn’t be put off by the restaurant’s immaculate white-tablecloth surroundings. With an entrance from a corner of the square via a flight of steps as well as from the gallery’s cloakroom, it also functions as a daytime café offering breakfast, coffee and some fine cakes such as fresh berry Napoleon (€5.40).

The restaurant operated one of the square’s popular outdoor terraces last summer. Until it gets warm again, enjoy the elegant interior. Take a seat on one of the curious greens and sparkly red armchairs-without-arms. The pricy-looking floor tiles and painted walls have similar tones, and street-level windows encircled in red brick let in some natural light. Grape-vine chandeliers adorn the vaulted ceiling.

The original architect of the building, Harald Julius von Bosse, was from a Baltic-German noble family who lived in St Petersburg. He was in his early 40s when the palazzo-style structure opened in 1855, and he later designed buildings in Dresden and Helsinki. Rīgas Birža, which reopened in 2010 after painstaking renovation, has been used as a stock exchange, an agricultural institute and, in the Soviet period, a library.

One dining option each working day between 12pm and the surprisingly late time of 6pm is the three-course set lunch (€12), which changes every two weeks or so and might include, for example, tomato and vegetable cream soup with noodles, a choice of Latvian-style pork fillet or cod, followed by apple and nut pie with caramel sauce, including freshly baked bread, citrus water and tea or coffee.

But we were not disappointed by our slab of sizzling beef (€24.20), which came with oven-roasted zucchini and bell peppers, a few leaves of ruccola and a little pot of thick red-wine sauce. As we ate in this evocative environment, drinking a soothing hot cocktail of Riga Black Balsam and blackcurrant juice, the syrupy sounds of Ella Fitzgerald conjured up a bygone era.

Other saliva-inducing main-dish choices include rum-marinated entrecote, also served on a hot stone, salmon in a honey-ginger sauce and gilthead seabream. Less expensive options include salads, pastas and soups – try the salmon soup with shrimps and cauliflower (€4.20). There’s also a long list of drinks.

The restaurant does banquets and group menus – there are up to 60 seats in winter – ranging between €10 and €40 per person. On any day, gallery visitors get a 20% discount off all restaurant prices – food and drinks. So combine a visit to one of the city’s premier art galleries with breakfast, lunch, dinner or a deliciously sweet snack.