In ghantaghar, multani chanp stall in front of multan kitab ghar is the oldest and famous as well. The sohan halwa market is behind the civil hospital going from fawara chowk to muslim high school. There are a couple of good halwa shops in Multan cantt main bazar also. You can also try qulfi near muslim high school or Baba ice cream near nawan shehr chowk.
If you want to be more adventurous then try fried fish or chicken piece at sheedan mushtaq in kotla tolay khan. The shop on the right coming from ghanta ghar is the authentic sheedan.
Try gol gappas in multan cantt. try Rizwan near shangrilla chinese. Breakfast here is the usual halwa puri, channay, nihari and paye etc. The better places again are near ghanta ghar. But I'm not very well informed about good breakfast places. If you like I can contact some of my friends in Multan to get the updated information.