Downtown Lincoln has many great places to eat in and outside of the Haymarket District.
The Haymarket is definitely worth a visit. There are many types of restaurants found here: Italian, Mexican, even Philippine, as well as several better pizza chains (Old Chicago and Green Mill), Lazlo's Brewery & Grill (710 P St, 402.434.5636) is a local favorite.
Additional places can be found on O Street a few blocks east of the Haymarket area. Recommended is Crane River Brewpub & Cafe (200 N 11th S on P St., 402.476.7766). It's east across the street from the Embassy Suites and the kitchen closes at midnight.
Finding a meal after a game is tricky since most restaurants and bars close their kitchens at 11:00 PM. Places like Crane River are rare since most locals will tell you they go to the "late night drive thru" at various fast food restaurants.
The Nebraska State Capitol is highly recommended. Unlike the "standard" domed building, this statehouse was built mainly during the 1920's in an art deco style (by Bertraum Goodue). This is the tallest state capitol in the country at 400 feet high with 19 foot statue of "The Sower" at the top. There are free tours and you can go to the top. During 2001 the building was undergoing repairs and maintenance shrouding it in a tall metal framework of scaffolding.
Though already mentioned repeatedly, the Historic Haymarket District. This is the "old part" of town next to the still active railyard. The area includes the post office and first city hall as well as several warehouses converted to shops and restaurants of many varieties. Several public works of art can be found while exploring the six (or so) blocks that make up the heart of the district.
One of the best times to go is Saturday mornings during the Farmer's Market on Saturday mornings (until 1 PM). Fresh produce, flowers, canned goods, original arts and crafts, even jugglers and entertainers can be found taking over the street.
On (or near) the University of Nebraska campus are several points of interest such as the U of N State Museum (Morill Hall, 14th & U, 402.472.2642) with its large collection of fossil elephants and a mammoth or the Sheldon Memorial Art Gallery and Sculpture Garden (12th & R, 402.472.2461) with its collection of contemporary American art.
Children may enjoy the Lincoln Children's Museum (1420 P Street, 402.447.4000) and its Prairie Dog Town, Tot Town, real airplane and Mack truck exhibits. The Lincoln Zoo (27th & B St., 402.475.6741) or National Museum of Roller Skating (4730 South St., 402.483.7551 ext 16) are other local options.
Embassy Suites (10th & P, 402.474.1111) is one of the closest and best places to stay in Lincoln when going to "either Haymarket." The Embassy Suites is also where the visiting stays --though they have to maintain decorum being in a truly fine hotel. It, and the Holiday Inn Downtown (141 N 9th. St,402.475.4011) are close to everything though rates tend to be over $100 a night. They are convenient if you're spending time in the district and using the connector where you can avoid the traffice and parking issues.
Many other less expensive motels can be found along I-80 and around the airport which is not far from the park.
When the college football season begins in late August and September downtown Lincoln is swamped by the crowd going to the Husker game at the 77,000 seat Memorial Stadium. Though the Huskers play Saturday afternoons, expect hotels to be booked with heavy traffic in the area. Every "Big Red" game has been a sellout since Nov 3, 1962! This means most every hotel and motel in the area will be booked months if not a year in advance.