Unfortunately, Sweetgrass is closed - according to a blog by a local food writer, the future is uncertain as the owners are looking for investors.
That area of Ottawa is the ByWard Market - lots of good restos there: Domus, Play, Navarra, Chez Lucien, French Baker (breakfast), Benny's Bistro.
West of the downtown core, I really like Wellington Gastropub.
108 Murray St, Ottawa, ON K1N5M6, CA
85 Murray St, Ottawa, ON K1N5M5, CA
93 Murray St, Ottawa, ON K1N5M5, CA
119 Murray St, Ottawa, ON K1N5M5, CA
137 Murray St, Ottawa, ON K1N5M7, CA