In Indore there are few places you must try. Go to 56 dukaan. Main shops I would suggest is Sam's Momo's, Jhonny hotdog, Dilli da roll, Oye paape is also good. For pasta and Maggie go to LIG Maggie and pasta.
You will get Paani Puri stall on every corner of the city, and believe me you won't get better than thele wali paani Puri in malls.
At night go to Sarafa.
Try Vijay Chaat ki khopra Petis, Joshi ka dahi bada, Sawariya ke chole Tikiya and bhutte ka kiss.
In ujjain there are few restaurants near the temple itself. But you should explore the street food there. It's good.