For a real treat, drive up into the Gatineau Hills for 20 minutes and go to Les Fougeres ( http://www.fougeres.ca/ ). Take King Edward Avenue north across the bridge to Hwy 5 in Quebec, then exit onto Route 105 north. Once you get past the car dealerships, it's the prettier route.
I'd recommend a few places: for pricey, go to Beckta, Domus, or the Urban Pear, The Works is a fun place to go for inventive burgers as the previous post states. Ottawa has a ton of good Thai restaurants, like Nokham Thai, Royal Thai, Bangkok Thai, etc... I've also heard good things about Whalesbone Oyster Bar, and Elgin St. Freehouse.
I'd recommend doing a search - you'll find loads of suggestions.
In the meantime, here are some ideas for places not too far from downtown.
Le Boulanger Français - awesome bakery and café, with a cute bistro in the back.
The Black Cat Café - fancy and funky food, slightly pricy but worth it (Domus is another place that fits that description).
Khao Thai - great authentic Thai food in fab decor. Hope you like it spicy.
Kinki - trendy Japanese place, more for the atmosphere and the drinks, but the food is good too.
The Black Tomato - next to the Courtyard, good variety of food (from Mexican to Asian influences) and cool hipsterish setting.
Kasbah Village - best Moroccan in town, great service and exotic decor. I think they have a bellydancer some nights.
Curries - cheap-looking place, but one of the few options for South Indian food. Good and inexpensive.
The Works - the most possible variations on the burger. Pretty expensive for what it is, but fun and tasty.
The Manx - if you want a pub brunch, this is where to go.
For an afternoon snack or lunch, there's the sconewich on Albert Street. Fantastic scones, tasty selection of sandwiches and soups. Really loved this place when I used to live in Ottawa. In the same area on Queen Street near the Delta hotel is Caffe Zucchero and they have nice pannini's, soups and salads so this is another viable lunch option.
As Mainja mentioned, there is the Courtyard restaurant and they do a lovely brunch on sunday's and you can take in the nice atmosphere of the cobblestoned courtyard on the patio. This courtyard is located just off George Street in the market. In the same courtyard, is Mamma Grazzi's a mid-priced italian restaurant that does some pretty tasty pasta's and thin-crust pizza. Further, near the courtyard is a coffe place called Planet Coffee that is a great place to relax with a coffee/beverage and one of their baked goods.
If you're looking for a really fancy dinner or a 'wow' me place, then I would suggest Beckta on Nepean street. It's been the place to go in Ottawa for a couple years now for high end dining.
Other places that might interest you are Bocado a mediterranean type place on Sommerset that has been getting good reviews, Sweetgrass Bistro (aboriginal cuisine)-in the market and one place I regret not trying when I lived in Ottawa. Best of luck and happy eating in the capital!