Russell's Steaks & Chops is the most consistently praised steakhouse in this area. It is in the suburb of Williamsville, on the busy thoroughfare Transit Road. The owner (Russell Salvatore) is a well-known local restaurateur/hotelier with several huge and opulent (gaudy, some would say) establishments.
After that, Black & Blue Steak & Crab, also in Williamsville, gets high marks.

Unfortunately, downtown Buffalo lost its premier steakhouse a few years ago (E.B. Green's). Buffalo Chophouse seems a good alternative if you want to stay within city limits. They have an elegant interior. And perhaps a bit trendier gastronomically would be SEAR, on a nice block of Delaware Avenue (the street with the most old style mansions)—just 2 or 3 blocks up from City Hall.

It's unfortunate that because of the low volume of posts about Buffalo on this board (almost everything is NYC environs like Westchester and Long Island; these groups should be separate), I don't check it often.

I hope you found some good chow, but let me burst your bubble a little: Buffalo is not known for its diners or its "sloppy sandwiches."

Both Lake Effect and Jim's SteakOut provide serviceable meals. Lake Effect is mainly a destination because of the quaintly authentic building/interior. As for food, it is pretty standard. Probably best to stick to the breakfast items. For a trendier diner experience, try Swan Street Diner, near Larkinville, which is not to be missed.

Jim's Steakout serves up the best Philly-style cheesesteak sandwiches in the area. You can get them any number of ways—I like their French dip the best. However, Philly cheesesteak is not this area's forte.

Where Buffalo truly excels currently is at newer ethnic cuisines, like Cajun/Southern (Toutant, Shango Bistro), farm-to-table/hipsterish (Black Sheep, Roost, The Left Bank, The Dapper Goose, Craving), Burmese (Sun), and Southwestern (Lloyd Taco Factory). Also traditional Italian: Tappo, Trattoria Aroma, Chef's, Mulberry Cafe.

Beware, because we now do poutine better than you guys: Allen Street Poutine Company.

If you must have roadside dive-y food, I would head to Lewiston for the Silo. For soft custard, Lewiston has Hibbard's, which is excellent. Also Buffalo and its suburbs have Anderson's (original in Kenmore) and Bill Gray's (Clarence)—these are small-scale, civilized fast-food chains, with great custard.

I've been meaning to visit Black Iron Bystro. It sounds great, but I'm not sure if your Mom will be game for a gastropub.

There's been a lot of commotion about the new incarnation of Bistro Europa, called The Black Sheep. It is larger, but you will still need a reservation. I loved it:

http://www.blacksheepbuffalo.com/#tbs

And Dinosaur BBQ opened in downtown Buffalo in late 2014. Very recommended. Call them about the parking.

http://www.dinosaurbarbque.com/live-m...

For Southtowns, I've been meaning to try the Ebenezer Ale House. It's been around a few years, but I only heard of it recently so maybe you haven't either. Once again, it might be too pub-like for your Mom:

http://ebenezeralehouse.com/

So the two solid tips I can think of now are The Black Sheep and Dinosaur BBQ.

I have only been to H of G once, about two years ago, but I liked it and would go back. The best and most popular dishes seemed to be Roast Pork and BBQ Duck. Plates of these were flying out of the kitchen and disappearing quickly. Good snow pea pods too. I tried an oyster dish but did not care for it. Maybe it was the sauce.

If any of you come to Buffalo, I recommend Miss Hot Cafe in the northern suburb of Amherst, on Sheridan Drive a couple blocks East of Niagara Falls Blvd. They have a huge selection with lots of authentic favorites and I have never had anything I didn't like. Their braised pork, served with bok choy and a boiled egg, is especially good (just be aware that they close for an hour between lunch and dinner, and are closed on Mondays). Also near there on Maple Road is Red Pepper, my favorite Vietnamese place. Excellent Beef Pho, roast pork with rice noodles, shrimp spring roll. Cheers, Canadian friends!

Don't skip Italian; if you have time to find the Lackawanna gem called Mulberry Cafe (tucked inside a residential neighborhood next to a closed industrial site on the southern lakeshore), it's a great place for lasagne, meatballs, ravioli, etc. Has been on DD+D. Homey atmosphere and great food.

For pizza, I recommend La Portas (owned by a Greek family) in the Northtowns suburb of Williamsville, near the corner of Klein and Hopkins. It will take a while to get a pizza there, especially on weekends, so it's important to call ahead.

I can second Dinosaur BBQ. Delicious food but there can be a long wait at popular times.

I have heard good things about Gate House as well.

If you might be in the mood for something more gourmet-ish (and the kids are pretty mature for their ages or at least able to act like it for a few hours), there is an outstanding "small plates" (tapas) gastropub called Good Luck Restaurant. It is a wonderful experience. Look at their online menu if you are curious:
http://www.restaurantgoodluck.com/ind...

As Indy noted, Abbott's custard is fabulous. Famous all over the region. Truly exceptional.

Bistro Europa has closed but it will reopen as "The Black Sheep" in a new location (Connecticut Street) soon. This reopening is much-awaited. I find that Tabree is not worthwhile, but I second most of TeacherFoodie's other recommendations, especially Sun Restaurant.

Also Blue Monk on Elmwood for European pub food and a great selection of brews on tap. Resurgence Brewery on Niagara Street for ales brewed in-house (practically while you watch) and some snack options in a beer garden setting. My foodie friends also rave about Martin Cooks, but I haven't been there yet.

[Oops--looks like I'm answering an old post. Oh well.]

I like Bing's for catering. They're in Amherst, right on the outskirts of Buffalo, and they do catering all over Buffalo. Especially good for mouth-watering appetizers, like crab cakes.

More expensive and trendier (with a guarantee of outstanding food) would be Torches for either catering or the rehearsal dinner. On Kenmore Ave, towards the Northern part of Buffalo. Highly recommended.

BTW I have not heard good things about Templeton Landing (mentioned by another respondent), and I haven't heard of the other places, except for Pearl St. Brewery, which is the go-to pub after sporting events. So that would be OK if you want a very casual ambience.

For hot dogs and other grilled foods, I would recommend Ted's over the other local chains named above (Anderson's Louie's). Ted's uses local Sahlen hot dogs, as do most of the others. However, their grilling set-up is "bigger and better" than the others. Also, Ted's has the best onion rings anywhere.

I don't care for beef on weck, but I'm sure that for this (and other hot "sliced meat" sandwiches, as well as for chorizo and Italian sausage), Charlie the Butcher's is the best choice. Near the Airport on Wehrle at Cayuga.

Anderson's has its strong points, mainly for the frozen custards and shakes. For meals, I do go there often with my family because of the variety they offer. They have "something for everyone" (I often opt for soup), especially finicky kids who want something bland. But bland doesn't do it for Chowhounds.

Hayes Seafood House, attached to Hayes Fish Market on Main Street in Clarence, is one place where you can make sure when you order that the fish they fry for you is fresh. Best variety and quality of fish and seafood in the region. As a dine-in experience it is no-frills. Still, the prices are high and the service is not always pleasant.

There is virtually zero commercial fishing for New York State markets from Lake Erie. It's all sport fishing in NY; only Ontario and to lesser extent Ohio still have Erie-based commercial fishing.

"Residential house" type eateries of Buffalo are fine if you want to feel like you're in a time warp, but I'm sure you will find their food very unremarkable. In this category: Schwabel's. Eckl's, Creekview.
Much more memorable in the "old-style" category is Ulrich's Tavern in the downtown. They have good German food and pub fare.
If the OP doesn't have the Cheesecake Factory or Hard Rock chains where they live, these are bona fide destinations for Canadians and other international tourists in Buffalo/Niagara Falls. Few Canadians hit the Galleria Mall (which is indeed open Labor Day, no problem) without sampling the Cheesecake Factory.