Location and ticket suggestions

A 4-day Swiss Pass purchased in Switzerland is 259 CHF ( roughly $270). So it must average out to 65 CHF of travel each day to be cost-effective, unless you simply want the convenience.

You can use the Swiss rail site SBB.ch ( rail.ch to go directly to English) to find prices. Input you start and end points and the next page will show route and time options. Pick one a push the red tickets at the far right in the line. On the next page, use the little drop-down menu to choose "no reduction" to see the full fare. You do not have to enter name or DOB just to see the price. You will find that the full Fare from Basel to Stechelberg is 73 CHF, so it may be worth using a pass day. But there might be City or Supersaver tickets available for your date of travel that would lower the cost, bringing it under the 65 CHF.

For your Männlichen hike day, you can find prices on the lift's website, www.maennlichen.ch. most Swiss tourist lifts have their own website where you can find information and prices. Just Google the name of the lift, or try nameoflift.ch

I did this much for you and found the cost of a ticket from Stechelberg up to Wengen (11.20 each way) and the cost of the lift up to Männlichen: 23 CHF. If you are walking back down to Wengen your cost without a pass would be only 45.20--- not worth using up a pass day. Especially since the pass would nay cover you as far as Wengen. After that you would pay 11.50 with the pass to ride the lift.

https://www.maennlichen.ch/en/wengenmaennlichen-aerial-cableway.html

Rigi and Pilatus: each has it's own website under its name. I could not find reductions for a Swiss Pass for Pilatus. If you did the Golden Round Trip a Swiss Pass would cover the boat, but the cogwheel train may be only covered 50%.

Rigi is fully covered with a Swiss Pass, including boats, cogwheel train, and cablecar.

https://www.rigi.ch/en/Information/Mountain-railways/Rigi-Bahnen/Online-Tickets-Rigi-Bahnen/Mt.-Rigi-Railways-day-ticket

The cost of the trip if you pay is 72 CHF, plus whatever the boats cost. Total is likely over 100 CHF.

I did not look up costs for Day 3--- train to Luzern and possible boat trips. You may not want to do the boat trips at all if you are riding boats the next day for Rigi or Pilatus. If you don't ride boats this day ( maybe it is raining, etc.) then the train trip alone is inexpensive travel this day.

So it appears it may not total up to the 259 CHF you would pay for the Swiss Pass.

If you add up the prices of the things I haven't figured, including possible travel to Zurich on Day 4 after Rigi or Pilatus, and it comes close, you can decide if the extra convenience of the Swiss Pass is worth it.

Nothing on your plan requires reservations. Pilatus is fully covered with the Swiss Travel Pass this year. I think the costs that Lola has outlined plus travel to Luzern and the fact that you would not pay extra on the cogwheel train mean you're getting pretty close to breaking even with the pass, and any little extras not already counted could put you over. I also think the convenience has value.

I agree with Laura that the convenience of a pass adds considerable value. We actually have not traveled in Switzerland without one, and love the convenience.