Hi Enigma-
1960man has offered his opinion of sightseeing at various locations. What is enjoyable for one person may not be for another, and vice versa. It is strictly personal.
I do think that your plan to visit the Rigi would be possible and relaxing. Keep an eye on the schedules…in detail. The last return trips by lake boat leave Vitznau at 1949, so you must leave Rigi-Kulm at 1900. That will give you plenty of time to make the trip, and walk around Luzern a bit if you wish. In theory, you could catch the boat from Luzern to Vitznau at 1712, arrive at Rigi Kulm at 1847, wait 7 minutes, and return departing at 1900. Of ourse, that would be a a very short time up top, so you could instead leave as late as 1612 and have an hour at the top.
In contrast to 1960man, I like to stay in expensive Luzern and enjoy a brief walk through the crowds of tourists around the old town. That part of Luzern is very small, as cities go.
My daughter and her young daughter ( age 8) enjoyed the Lion monument (which is about a 10 minute walk from the main station and also from the old town) and found the nearby Bourbaki Panorama fascinating.
http://www.bourbakipanorama.c h/en/
de.wikipedia.org/wiki/ Bourbaki-Panorama
I made a photobook about our trip, in 2009, and have attached two pages.
There is bus service:
map.search.ch/?pos=666521,211782&z=25 6&poi=haltestelle,zug
Mouse over a bus icon for route numbers. Click on icon for near term timetable. The bus stop that I have circled on the attached screen grab is called Luzern, Löwenplatz ( Lion Plaza or Lion Square). The map is supposed to accept markups, but they would not take for me, so I added a screen grab and marked it up….attached. Since the forum software does not allow removing attachments added by mistake, there are two screen grabs. One is marked up; one is not and can be ignored.
We always enjoy eating at restaurants along the river.
http://www.rathausbrauerei.ch /en/ and ,
http://www.luzern.com/en/thin gs-to-do/eating-drinking/restaurants/r estaurant-schiff/
schiffluzern.ch/en/
And, the attached view (at dawn from the Hotel Schiff – now made into apartments) is a benefit on a sunny day. Similar views can be had from other hotels along the river. All are popular with tourists, and can be quite expensive if you get a room with a river view.
Slowpoke