Around the main square and along the central streets there are several small cafés and canteen-style eateries serving Armenian staples: soup, grilled meats, salads, fresh bread, strong coffee. These are working-local places rather than tourist restaurants, with prices to match. If you are just passing through for the churches, a stop at one of these for coffee and a snack is the easiest option.
The town's bakeries sell lavash and gata (a sweet pastry filled with sugar and flour — one of the regional specialities). Ashtarak gata is considered among the best in Armenia and worth picking up to take back to Yerevan.