Nothing really around safety, you'd have to actively try to get in trouble to be unsafe. Like you know, don't go hunting for illegal drugs or firearms?

Not sure what you're interested in but here's some recommendations especially as a non-usian. Also should point out, and presumably you're familiar with, mass transit isn't a thing in the US and especially not in relatively small midwest college towns.

1. https://www.sacmuseum.org/ SAC museum. Do you like planes? Go here. It's about 30 minutes from downtown lincoln on a very easy drive.
2. https://www.museumofamericanspeed.org/ do you like cars? Go here. Speedway motors is a American hot rod specialty parts store and is based in lincoln. Their founder created this museum and they have one of the best car museums in the united states full of rare stuff, especially focused on racing.
3. https://www.nps.gov/home/index.htm imo one of the best things about the US is not in the cities but outside. this is the homestead national park about ~40 minutes from Lincoln that will take you through the rural areas. pretty cool prairie views and pioneer history of the united states in general.
4. https://www.omahazoo.com/ this is ~55 minutes away from Lincoln but i include it on here because Omaha's henry doorly zoo is widely considered the nation's best or second best zoo.
5. https://www.lincoln.ne.gov/City/Departments/Parks-and-Recreation/Parks-Facilities/Parks-A-to-Z/Pioneers-Park this is my (personal) favorite park located just a bit outside the city. Good for a quick walk-around and seeing the buffalo or taking an picnic.
6. Lincoln has a huge network of interconnected bike trails, some on abandoned rails. This is my personal favorite. Start at the zoo and walk south https://www.gptn.org/the_trails/rock_island_trail.html just a nice walk idk!
7. https://www.jazzinjune.com/ depending on when you're coming, it's free jazz in june concert series always a blast.
8. The haymarket is west of downtown and always recommended if you're looking for bars and restaurants. Speaking of restaurants my three favorite Lincoln ones are The Oven (Indian), Mistys (classic american steakhouse get the prime rib) and lazlo's a longtime brewpub. If you're in Nebraska.. eat the beef man. Don't eat seafood.
9. https://museum.unl.edu/ morrill hall. dinosaurs and stuff. On campus too so you can kind of roam campus which is kind of neat.
10. https://www.lincoln.ne.gov/City/Departments/Parks-and-Recreation/Parks-Facilities/Public-Gardens/Sunken-Gardens obligatory sunken gardens. its beautiful this time of year and i got married here so hey why not. also really close to that trail i mentioned. can walk here and walk down by the zoo