Hi Sayantani -
Your hotel will put you very close to the old town, and may have a door way into the town, if it is on the Rathausquai across the river from the Jesuitchurch. If it is the Hotel des Alpes, the rooms are nice, the kitchen is mediocre. Or, was. when I have stayed there. My guess is that the kitchen is sort of "dumbed down" for less discriminating travelers.
You be very close to the Rathaus Braurei restaurant.
This website gives a tremendous amount of information about the lake boats, with many detailed links in it. There are detailed schedule pages, note seasonal changes. In the details you can see which boats have restaurants.
Also, if you scroll down the home page to the dark area you can see a couple of useful maps of the lake region. They don't seem to show the boat routes.
If you use the advanced search section of the timetable, restrict the journey to ships, get a list of journeys, click on the "+" to the left of a journey, and click on map in the footnotes, in theory you should can get a map of the lake boat route. I have not fully mastered that process. Ibn practice, sometimes I get a very useful map, other times a useless line,no map.
[Some other maps-
The first attached image of this thread shows a map of southern part of the lake with lake boat stops:
Mapsearch is good to use, because it can show transport stops. I have turned on an overlay under "Points of Interest/Traffic, which show different train routes and stops. You can add buses. Not sure how to add boats.
This extremely detailed map shows the boat docks around the lakes, as well as their proximity to rail stations, etc.
map.geo.admin.ch/?topic=ech&lang=en&bgLa yer=ch.swisstopo.pixel karte-farbe&layers=ch.bav.ha ltestellen-oev,ch.swisstopo.swiss tlm3d-wanderwege&layers_visi bility=false,false&X=2 10810.00&Y=667030.00&z oom=6
The tourist info office at track #1, Luzern Main Station will have a good map, I'm sure.]
In that "dark" section of the timetable, you can find out which boats start from which towns, a list of the ships, etc. Some of it is only in German, 'Dampfer" refers to a paddle wheel steamship.
Look on the schedules pages, noting a schedule change on September 12. Every route is shown.
A good short trip- If you scroll down the main schedule page, you will see the approximately one hour runs to Alpnachstad, which dock a few feet from the railroad station for a train back to Luzern. That also is the base station for the cograil to Pilatus. That route is a good short one. I suspect that the largest boats don't get all the way to Alpnachstad, so that run may use some of the smaller ones.
Other short ones have small separate timetables, as well.
The boats to Vitznau take hour, but Vitznau is only connected to Luzern on land by bus+train and is a significantly less simple return. The best return is by boat, repeating your journey in the reverse direction.
If you wish to make a longer trip, you could take the boat to Vitznau, the cograil to Rigi Kulm ( the top) and return by several routes Elapsed time of about half a day:
If you were to take the boat ride from one end of the lake to the other - Luzern/Flüelen, it would take about 3 hours. The train station at Flüelen is a few meters from the boat dock. Could do train one way. Figure 4 or 5 hours total. The time table would help with the trains.