There's a lot to pick in the Market area alone. I second Murray Street and Play. Also in the Market and worth considering are Sweetgrass (aboriginal), Domus and Navarra (contemporary/Spanish).
Something in the downtown core, but not in the Market, is Town. It just opened up and I've heard very good things about it. I haven't been yet but can't wait to go. It's on Elgin Street.
108 Murray St, Ottawa, ON K1N5M6, CA
85 Murray St, Ottawa, ON K1N5M5, CA
110 Murray St, Ottawa, ON K1N5M6, CA
93 Murray St, Ottawa, ON K1N5M5, CA