Hi,
I have stayed in the Gare de Lyon area three times (the last in 2018) and have enjoyed it. It is clean and I always felt safe. When I was there in '18 I do recall some significant construction going on, but nothing that impacted my stay (I'm a male, solo traveler and usually stay in 2-star hotels).
I don't think there are any "must sees" immediately around the station, but the Gare Austerlitz is just across the Seine River, as are the Jardin de Plantes, the Arena de Lucete, and the Sorbonne. I'm a very big walker, and I love walking through Paris, so these are all in walking distance to me. I like to get out of my hotel early, so I enjoy walking to the River and heading up along the quai to the Isles St. Louis and Cite. Other times, I'll walk up the Rue de Lyon to Bastille Place and turn left onto Rue de Rivoli. Also nearby Gare de Lyon, on the same side of the river, is the Place de Vosges, St. Paul's Cathedral, the Isle de Saint Louis and the Place de Bastille.
Even if you're not a big fan of walking, you can get anywhere fairly quickly on the Metro and there are plenty of stations within walking distance.