Luzern is great, touristy things include the nearby
Pilatus and
Rigi mountains, which can be hiked up for free, or got up via cog railways and cable cars, the old town which is nice to walk around and maybe shop, but truth be told, it's not so big, very pretty though. Boat trips on the lake are also a nice couple of hours out.
You could find yourself a pub/cafe by the river or the lake and chill while soaking up the scenery, might even be warm enough to swim in the lake or just explore around town, plenty of things to find.
Blue Balls festival is coming up, they have free concerts outside during the day with the usual festival stalls selling a variety of stuff, food, beer, trinkets etc. Can get quite busy, but a lot of fun I find.