Plum's restaurant in the Mayfair Mall up the bluff from the park had a great Sunday breakfast buffet, but they're gone. There's a Valentino's restaurant just across the river in So. Sioux City which has an all you can eat pizza buffet that's OK for a meal. For the "best pizza in the midwest" I'm told to go downtown to Buffalo Alice. Otherwise I don't have any particular recommendations.
James Murray (who does live there) says there's lots of good restaurants up the hill like Applebee's or Sizzler. But he recommends Garfields in the Southern Hills Mall, which I did try and enjoyed.
The big attraction here is gambling. Here it is restricted to the paddlewheeler Bell that travels up and down the muddy Missouri during the morning (8-10 AM). During the rest of the day she's docked for (Keno) gamblers.
Other activities may be crossing the river into Nebraska (just to say you've been there) or up the road into South Dakota (or just look at its southeastern most tip between the rivers). We went to the mall and watched movies when we weren't feeding the players.
Reservations are highly recommended as people trek here on weekends to go on the gambling paddleboat and they may fill any given weekend. Newer hotels in the vicinity of Lewis & Clark Park may help ease this problem.
Several motels are off Singing Hills Blvd. including the Baymont and Days Inn. Up the hill from the park (off I-129 or Singing Hills Blvd. on the bluff) you will find several mid to low-price motels with indoor pools like the Fairfield Inn (712.276.5600, 4716 Southern Hill Dr.) and Comfort Inn.
Otherwise the usual places are a couple miles north in the city. There are some one-star variety motels on one of the roads to the local (Briar Cliff) college where I've stayed that were all right "in a pinch."