Hi Tamival, and welcome to MySwissAlps!
>> Working on itinerary after disembarking from River Cruise in Basel the end of April, 2018 into early May.
At this time of year, some mountain transport is not operating, due to seasonal closure or maintenance. If you can provide exact dates, we can let you know what will or will not be operating.
>> Two couples wish to explore the Alps Region for 4 - 5 days ... Thinking of Luzerne and Geneva (Lausanne?) as possible places to stay and do sightseeing from there. Feasible? Or should we look at Zermatt in order to fully experience the area?
For the time you have available, I would normally suggest splitting your time between Luzern and the Jungfrau Region (Grindelwald, Wengen, Lauterbrunnen, Mürren). However, depending on your exact dates, much of the mountain transport in the Jungfrau Region might not be operating, in which case Zermatt might be a better alternative for mountain experiences. Geneva and Lausanne have less to offer the first-time visitor in my opinion.
You can use the Swiss Timetable to see how long it will take you to travel from one place to another:
>> Weather/time frame - in looking at hotels, sights, etc., it seems we may not be able to do some of the areas (Mt Pilatus etc?) Many hotels seem to be booked or unavailable at this time frame.
You are coming in the low season, so some hotels will be closed. However, it may well be that many hotels have not opened their bookings for April/May yet. I would not expect you to have any difficulty in finding accommodation.
In Luzern, the Pilatus cogwheel train will probably not be operating, but you can go up and back in the gondola and cable car between Kriens and Pilatus Kulm. The Rigi cable car between Weggis and Rigi Kaltbad will not be operating, but you can still go up and back in the cogwheel train from Vitznau or Arth-Goldau. The Titlis gondolas will be operating.
>> Travel from Basel to Luzerne/Geneva and back. Are there direct train options? Can we do all trains for transportation? I've looked but can't see this option so may be looking in the wrong place.
There are direct trains from Basel to Luzern, and some that involve a transfer in Olten. Trains from Basel to Geneva require at least one change, which varies depending on the departure time you choose. The train network is very dense, which will be apparent if you look at the validity map for the Swiss Travel Pass, on which train routes are shown in red:
This page has further information to introduce you to rail travel in Switzerland:
www.myswissalps.com/tr ain/practical/howtotra vel