I suggest you to try Robin Pub (83, Alexandru cel Bun street), it's right in the center of the city, below the cathedral. It is a British style pub/restaurant with a great Caesar salad.
If you like to drink a lot of beer you certainly and logically should go to German style "Bier platz" (55, Mihai Eminescu street)
If you have kids and personally want some cookies or ice cream - go to "Delice d'Ange French Bakery" (117/2, 31 August 1989 street; Reservations: for children's parties or group celebrations, please call +373 (22) 24 14 28 ). Another place, but not so quiet&nice...anyway acceptable is Andy's pizza (http://www.andys-pizza.com/) that have a great playground for kinds (152, Stefan cel Mare bl)
For a cup of coffee go to Coffee Beans behind the Patria Cinema (103/2 Stefan cel Mare bl)
For other places check this link www.allmoldova.com/en/catering/catalog.html.
Good luck and enjoy your meal/beer/cookie or coffee!