Hi swap095 -
<<"I see that Lucerne hotels are quite costly. Need some suggestion on places to stay around Lucerne which is well connected by train and nice to stay.">>
I am not sure what price range you are seeking.
Luzern is quite popular and the hotels can charge accordingly. Your suggested approach is a good one, and both train and bus service should be considered.
You might look at these links:
as well as
Also, your request will get better attention if you post it in the forum section:
When I have had to look for accommodations meeting your criteria in years past, before this form became available, I would open up this map:
map.search.ch/?poi=haltestelle,hotel, zug&pos=669464,211480& z=64
in which I have used the menu for points of interest, and turned on overlays for "accommodation" which, strangely, is under "gastronomy" and also "Traffic" to show train and bus stations.
Then I would start looking in the surrounding villages and towns. The icons can lead you to accommodations in various town. That is a very slow and tedious way, and takes a lot of time, but it could be a last resort. Places around the lake tend to be more expensive, because of the views. Places north of Luzern have less "touristic" features, and that might be a region to start in.
If you zoom in on that map, you can see the rail lines.
You can also check AirBNB, which this forum does not support, and use that map that I linked to for help in finding the locations of the places that pop up. and public transport.