>> it's looking like it will work out for us to be in Switzerland for either May 17-19 or May 23-25. We are interested in doing the panoramic walk from Mannlichen to Kleine Scheidegg but I believe I read that the gondola and cable cars will not be operating until June, with the exception of the Pentecost/Whitsunday weekend. Are there other ways to get to Mannlichen, and will that trail even be open at that time? I have read that there will still be snow in mid-May.
One of the forum experts on Wengen, Kim, says she has never seen the Männlichen-Kleine Scheidegg walk open before 12-15 June. See her post of Jan 16, 2018 - 6:28 AM on the following page:
The trail is groomed for winter walking, but I would not expect the grooming to continue once the cable cars shut down on 3 April for between-seasons maintenance.
The cable car from Wengen to Männlichen reopens on 1 June.
The gondola from Grindelwald Grund to Männlichen opens on 26 May, but if snow conditions are good, will also run on Sat, Sun and Mon 19 May–21 May.
Even if the gondola is running, the trail from Männlichen to Kleine Scheidegg might not be open. The local tourist office can advise you about which trails are open when you are there.
>> Can you also advise as to what might be a good "base" for our stay in Switzerland? We are considering Interlaken simply because it seems close to the Mannlichen hiking trail and we'd also like to go to Jungfraujoch. Today I have been reading more about Lucerne and that would be a nice place for us to see too!
For such a short stay, I would stay in one place only. If you are going to the Jungfraujoch, I would stay in one of the local villages (Wengen, Lauterbrunnen, Grindelwald, Mürren). Interlaken is another less scenic, less charming possibility.
Staying close to the Jungfraujoch will give you maximum flexibility to get up there when the weather is clear. Travelling from Luzern introduces the risk that the Jungfraujoch might disappear into the clouds during the time it takes to travel from Luzern to the Jungfrau Region.
You can check the webcam to see what conditions are like before buying a ticket to go up: