I actually don't know of a Qatari restaurant in Qatar. Local food I believe is Arabic food in general I think. The Lebanese restaurants are good example of this. As for walking distance, well Katara is probably your best bet if you are a strong walker and don't get killed on the roads on your way there. Best pop down to the lobby and get a limo over there, it shouldn't cost much as it's so close. But a word of warning; Katara's restaurants are among the best, and as such are very expensive.
"I would like to experience local foods"
I actually don't know of a Qatari restaurant in Qatar. Local food I believe is Arabic food in general I think. The Lebanese restaurants are good example of this. As for walking distance, well Katara is probably your best bet if you are a strong walker and don't get killed on the roads on your way there. Best pop down to the lobby and get a limo over there, it shouldn't cost much as it's so close. But a word of warning; Katara's restaurants are among the best, and as such are very expensive.