I would recommend Willy's Eatery ( http://willyseatery.com ) It's a total mom & pop shop with great Greek and American food. They have the best Egg's Benedict in town and have bunch of really good Greek Wraps and Gyros etc for the lunch crowd. The place is always packed when I go but the service is very quick...
2101 E Ball Rd, Anaheim, CA 92806
Anaheim's forte is not farm-to-table Californian; it's really more about ethnic dining around here.
The White House is the local choice for Italian; Park Avenue in Stanton grows some of their own vegetables and their own olives. Cafe Hiro in Cypress is an excellent Japanese bistro (make sure to reserve, it's quite small) and Gabbi's in Orange is a good place for a nice Mexican sit-down with attention paid to the ingredients. Xanh Bistro in Fountain Valley, Quan Hy in Westminster, and S Fine Dining in Westminster are nearby-ish Vietnamese upscale places. While Olive Tree is in a mini-mall, it's an excellent destination for Middle Eastern dining (the owner is Palestinian and the chef is Jordanian—this is not your average kabobery). Just make sure to ask about the specials. Thai Nakorn is one of the best Thai restaurants in the region and is just down the street in Garden Grove; same deal, order from the specials menu.
If you want more middle- and low-end places, let me know; Anaheim is chock full.
Park Avenue Restaurant
11200 Beach Blvd., Stanton, CA 90680
10509 Valley View St, Cypress, CA 90630
Thai Nakorn Restaurant
12532 Garden Grove Blvd, Garden Grove, CA 92843
Quan Hy Restaurant
9727 Bolsa Ave, Westminster, CA 92683
16161 Brookhurst St, Fountain Valley, CA 92708
512 S Brookhurst St, Anaheim, CA 92804
White House Restaurant
887 S Anaheim Blvd, Anaheim, CA 92805
I just had lunch at Merhaba (after way too long a break from my last visit), an Eritrean Restaurant not too far from Disney. It is a hole in the wall that is definitely going to be different. They have a good variety of vegetarian dishes if you need that, and getting a group to eat with their hands out of a big communal plate is just fun.
E A Merhaba Shop & Coffee
2801 W Ball Rd # 5, Anaheim, CA
There are a few places next to the Anaheim Convention Center. Mr. Stox about a mile east of ACC on Katella. You also have Mortons and Ruth Chris near by. At the Garden Walk, you have Roy's. In the Disneyland area (I know you said NO DISNEYLAND) you have Catal (Downtown Disney) and Napa Rose at the Grand Californian Hotel.
Napa Rose Restaurant
1600 S Disneyland Dr, Anaheim, CA 92802
1105 East Katella Ave., Anaheim, CA 92805