Tulsi,
I was in Lucerne recently, so have a few suggestions....
As suggested in a previous reply, hike the wall of the old part of the city. This is a relatively easy walk, but only part of the wall has been restored for hiking. The location provides an interesting vantage point for photos of the city.
Take a day cruise on the lake. That would allow you to see some of the surrounding communities from the water, and also a great opportunity for photos (providing the weather is good).
Although it's not "hiking or outdoor", the Museum of Transport is very interesting, and it's very easy to spend four hours or more there.
Take the local walking tour. Tickets and details available at the T.I. (which is in the train station). The tour that I took was conducted in both German and English. That provides an opportunity to learn something of the history of the city.
Take a walk to visit the "Lion of Lucerne" monument. As Mark Twain noted, it is a very "moving" piece of rock.
Ask the T.I. about other local hiking options.
Just explore the town. It's beautiful!
Happy travels!