<<"Mountain excursions & local sightseeing only. Thanks.">>
Arno has pointed you to best first place to look.
Pilatus is close to Luzern, accessible by train or by lake boat, and is a really impressive cog rail ride. There are great views from up top, but not a whole lot of walking around space. Some restaurants/hotels.
I attached one very old photo taken going up to the top of Pilatus.
The Rigi is a much gentler mountain. More room to walk around, more hotels/restaurants at different locations, several different ways to go up and down. Also very nice views.
I remember my first visit to the top of the Rigi (Rigi Kulm) about 30 years ago. It was a kind of cloudy day, and I was at the top watching a sailplane appear and disappear as it flew around the mountain at alevel lower than my viewpoint.
I have not been to Titlis. It is a bit further away than Pilatus.
If a like boat ride interests you, there are various routes, so you can focus on the northern parts of the lake or ride from one end to another.
If I am taking a lake boat, i always pick up the printed schedule brochure and study the various criss-crossing route options, as well as which stops give me bus/train access back to Luzern.
The brochures are available at the ticket counters at the various stops, or from the very good tourist information office by track #1 in Luzern Main Station. (Hauptbahnhof). They can also offer sightseeing suggestions.
One which I and my family and friends have enjoyed is not far from the famous Lion of Luzern. I don't recall if this web site mentions it.
It is the Bourbaki Panorama.