In this area, they'll be generally simple food, such as noodles, or grill fish and miso soup etc., and found mostly within walking distance of the JR stations.
I might as well combine shopping and lodging tips here as they would also be found in the same places. Shopping includes fish bait, usual sundries, and as for local specialties, wasabi roots, or pickled wasabi, etc.
Just to the east of Ome Station, down what is clearly a side street, is Japanese/Chinese noodle restaurant. Based on the Google translations, the name is something like "Enjoying Oneself with Others" (偕楽).
We had dinner here on Sunday night, primarily because it was one of only two or three restaurants open near the Ome Station. We were a bit cold and hungry after a short trip around Lake Okutama, and ramen sounded perfect. We scanned the plastic food models in the glass case, then we entered and took a table by the window. The friendly waitress greeted us in surprisingly good English, then apologized for not having menus in English. We had already decided what we wanted to eat, so no problem. We ordered a beer and two bowls of ramen. My ramen was covered in delicious vegetables like onions, carrots and bean spouts, with a few small pieces of meat for flavoring.
As we waited for the food, the waitress came back out and told us about their nice little restaurant that makes its noodles fresh on premises each day. She also mentioned that her daughter was going to school in New York City.
Very friendly place and very affordable at about 500-800 Yen for ramen or soba.
Kotobuki Happy Home is the rough translation of the Japanese name 寿々喜家 of a great little restaurant in Ome. Kotobuki also means "wishing for longevity" or "blessing to one's longevity." The restaurant was established in 1901, so it is celebrating its own longevity. The current structure was built around 1930.
The restaurant is famous for its unagi-jūbako, or unaju, eel over rice in a lacquered jūbako box. Unaju is said to have originated in the Edo Period, and it consists of a rectangular box filled with steamed rice and topped with filets of grilled eel glazed with a sweetened soy-based sauce, called tare. The eel at Kotobuki is always fresh, never frozen, and the sauce is a family secret.
We stopped here after a day of hiking nearby Mount Mitake. We entered the busy restaurants and sat at one of the Japanese-style tables on the floor. After scanning the menu, we quickly decided on two of the eel specials. The food was ready in 10-15 minutes, and the eel came with a bowl of mushroom soup and a small plate of pickled vegetables.
The portions were small, but the eel was tender and delicious. The price was a bit steep at around 2,500 yen ($25) per entree.