Hi devregi85 -
That looks like a well -organized itinerary. Perhaps a bit heavy on time in Zürich, but we don't know your arrival and departure times. If your departure time on 30/9 is mid-day or later, possibly even late morning, and very nuch depending on your interests, you might consider extending your stay in Luzern to include the night of 29/9. There are direct trains from Luzern to Zürich Airport every hour at xx10 all day long starting at 0710, taking 1 hour and 3 minutes. In between, at xx35, starting at 0635, there are trains every hour at xx35, requiring a change of trains in Zürich main station, taking 1hr 7 minutes.
And, if you miss the 8 minute connection in Zürich main stationdue to hauling luggage, for example, there are on the order of 6-8 trains per hour , depending on time of day, from Zürich main station to the airport.
Of course, if you have chosen specific things that you know that you want to see or do in Zürich,
then your plan as written may well be a better choice.
<<"Of course, we can get this info via swissalps webpage but we would like to know if there is any "must visit" spot.">>
To give more help on this point than we did earlier in the thread, it would be helpful to understand your interests.
For instance...do you want to hike? See museums? Ride scenic trains? Visit "old towns" in various cities? See the Alps? Take a boat ride on any of the beautiful lakes? It is not clear to me what you might consider to be a "hot spot." And there might be cold spots by late September, especially in the high Alps. ;-)
One Example -
For myself, and for some of my family members (whose tastes I understand), the answers are:
The Rosengart collection in Luzern, and Reinharts am Römerholz in Winterthur.
For others, it is this hike:
or this one:
For others, it is Restaurant Kronenhalle in Zürich, near Bellevue, and the tomb of James Joyce near the Zoo on Zürichberg.
As noted previously by Lucas, there are lists to help guide you.