Even those who don’t stay at the hotel should take breakfast or coffee at the Confitería Touring Club (Avenida Fontana 240, tel. 02965/43-3998) to partake of its timeless ambience. Sugar (25 de Mayo 247, tel. 02965/43-5978) is a sandwich and short-order option.
La Bodeguita (Belgrano 374, tel. 02965/43-6276, lunch and dinner daily) serves good pasta (particularly cannelloni) and pizza, with decent service.
The best new choice on the scene is 
Eloisa (Belgrano 351, tel. 02965/43-1606, www.eloisa.com.ar [1], US$10–15), a parrilla-restaurant with Patagonian flair in its meats, seafood, and even the wine list.
About three blocks north of Plaza Independencia, in an elegantly recycled flour mill dating from 1910, El Viejo Molino (Avenida Gales 250, tel. 02965/42-8019, lunch and dinner daily, US$10–20) is Trelew [2]’s most ambitious restaurant; its best dishes are variations on the traditional parrillada as well as pastas.
For ice cream, try Mares (25 de Mayo 195), and Vía Roca (Belgrano and Roca).
Roger Shop (Moreno 463, tel. 02965/43-0690), Trelew’s only Welsh teahouse, is the place to purchase traditional black cake.
Links:
[1] http://www.eloisa.com.ar
[2] http://www.moon.com/destinations/argentina/southern-patagonia/coastal-chubut-province/trelew