Omaha and Lincoln have crime rates that are roughly on par with similarly-sized cities; crime rates do vary considerably among neighborhoods in Omaha.
In Nebraska, especially in Lincoln and Omaha, there has been an increassing number of gangs. That should be something to which you should be alert, but generally they don't bother too much.
Severe thunderstorms, hail, and tornados are not uncommon during the spring and summer months; Nebraska is in "Tornado Alley". Stay informed of current conditions if severe weather threatens, as conditions can change very rapidly. Nebraska TV and radio stations provide excellent severe weather coverage. You might want to check the Tornado safety page if you are visiting Nebraska.
During the winter months, blizzards and ice storms do occur, and dangerous wind chills are a possibility. High winds can take even a limited amount of snowfall and form very large drifts -- beautiful to look at, but dangerous if you are stuck far from help. It is important to find a local weather forecast whenever you plan to travel through the more sparsely populated areas of the state.
talk
The vast majority of Nebraskans speak American English with a neutral "Standard Midwestern" accent. In some rural areas of the state, people speak with a slight accent best described as "country twang"; this accent is also easy to understand. Nebraska is largely devoid of unusual terms for everyday items, with a few exceptions:
Carbonated drinks are nearly universally referred to as pop.
Beer served from a keg at a bar is a draw; a half beer/half tomato juice drink in rural areas is a red draw.
The town of Norfolk is pronounced Norfork and the town of Beatrice is pronounced Bee-at'-riss
The town of Papillion is pronounced Pap-pill'-yun.
The town of Plattsmouth is pronounced Platts-myth.
Nebraska has a fast-growing Hispanic population, largely concentrated in its medium-sized cities and Omaha. In these areas, governments, businesses, and community organizations often provide services in Spanish.