There is an extensive array of restaurants in Northbridge. You will find a great selection of Southern European and Asian restaurants. Northbridge gets very busy on Friday and Saturday nights as Perth goes into party mode. Neighbouring Mount Lawley and Highgate also has some good options.
Fremantle is a good eating option. Famous for its cappuccino strip lined with cafes next door to one another popular with the yuppie crowd. On weekends, a local tradition is to visit the Fisherman's Wharf on warm, sunny weekend evenings for fish and chips. There are a couple of options to choose from close to the beach. Just follow your nose or the seagulls.
Subiaco is located just a couple of kilometres from the city centre. Subiaco is a trendy but fun suburb which features some great food and entertainment.
Claremont is a suburb on the Fremantle railway line where you will find some good restaurants as well (including authentic Italian).
The Swan Valley, especially along West Swan Road contains various wineries and restaurants with stunning views over the vineyards. Particularly good are The Black Swan Cafe, Duckstein Brewery, Elmar's and The Mallard Duck Cafe.