Switzerland Itinerary

Initially, I'd say too much time in Basel, unless you have other reasons. Also, too many days in Zermatt , IMHO. Use those days in the Berner Oberland. I'd also recommend staying in Lauterbrunen, Wengen, or Murren ( but a bit concerned about construction in Murren.) If you're going to the Alps, why not stay in the Alps, not just looking up at them.? Interlaken is a more of a transit center.
St Moritz is a glitzy town with high-end shops that are everywhere. Perhaps Pontressina instead?
Have a great trip in this beautiful country and safe travels!

https://community.ricksteves.com/travel-forum/trip-reports/lucerne-62eb4d28-60ab-4837-b4b4-91a2486eb732

Perhaps my 2021 trip report will have some helpful info.

When we planned our trip to Switzerland friends all told us not to stay in St- Moritz, rather in nearby, charming Pontresina with its decorated homes. We were so glad we did! We took a day trip to St-Moritz which confirmed that Pontresina was a much more appealing place! There is a short connecting train line between the two.

From Lugano to Zermatt you could use the scenic Centovalli railway, which connects Locarno ( a short ride from Lugano with Domodossola on the main line up to Brig, where you can change to the train to Zermatt. The route is fully covered with a Swiss Pass even thoughnDomodossolanis innItLy.

https://www.myswitzerland.com/en-us/experiences/vigezzina-centovalli-railway/

You can see on this map of the Swiss railway system that this is the most direct route:

https://cdn-doc.myswissalps.com/docs/default-source/rail-network-maps/swisstravelpass.pdf?sfvrsn=7788603a_56

Regarding Basel, it’s a great base for day trips. Freiburg, Germany; Colmar and Strasbourg, France; and Bern, Switzeralnd are easy day trips to take by train. We also really like Basel because it was not touristy at all. If you keep your 3 nights there, which is only 2 full days, I don’t think you will be bored.

The Schweizerhof in Basel is a great hotel if you are in need of one.

Basel is very pretty, I'm glad you have it on your itinerary. However, 1.5 days would do it. I highly recommend staying in the mountains as opposed to next to them( i.e. Interlaken), recommend 4 nights, Lauterbrunnen, Lauterbrunnen valley, Murren or Wengen. In terms of days, I'd try to carve out another day for both Luzern and Menaggio.

Wonderful suggestions and thank you for the link to the train from Lugano to Zermatt. I originally had Pontressina instead of St. Moritz but I wasn't sure about getting from Zurich to Pontressina by train. Suggestions and I will change that. Maybe I'll add a day at Menaggio and one less day in Zermatt. The reason for additional day at Zermatt was for a little down time. We are staying at Grindelwald and not Interlaken. I had thought about Murren but again connections and the amount of walking with luggage. Grindelwald seemed like a good area to stay. More time in Basel for some day trips and a tennis tournament. Thank you for all your ideas it really helps with planning.

Zurich to Pontresina is easy, a trip of 3.5 hours. It can be done with a single change at Chur, departing Zurich at 12:07. This one connects to the first part of the Bernina Express at Chur.

There are earlier departures with 2 changes. Either way, make sure your route goes via Chur so you are on the Albula railway across the famous Landwasser Viaduct:

https://en.wikipedia.org/wiki/Albula_Railway

https://en.wikipedia.org/wiki/Landwasser_Viaduct

We like Basel a lot, and it will be great to see a tennis tournament there. (We attended the Swiss Open when it was in Gstaad in July 2007).

Regardin oct. 8: Your plan is hopefully not to go to Lugano and than back track to Menaggio? Better take the train down to Varenna and the boat across.

WengenK has a good point about getting to Menaggio. Instead of taking the bus section of the Bernina Express from Tirano to Lugano, just take an Italian train from Tirano station south to Varenna, and ride the ferry across the lake to Menaggio. It is a nice and scenic 15-minute boat ride.

I will also mention an alternative scenic route reach Zermatt, which I think might be better than what I suggested above. From Locarno, take the hourly Treno Gottardo north toward Luzern, but disembark at Göschenen and change to a train heading back south a short distance to Andermatt. There you can catch either the Glacier Express direct train to Zermatt, or one of the regional trains running on the same tracks, likely with a change at Brig before reaching Zermatt.

https://www.myswitzerland.com/en-us/experiences/treno-gottardo/

Just make sure you are on a true Treno Gottardo regional train, not one of the fast trains using the deep Gotthard Basistunnel. Look for a train that actually goes directly to Göschenen with no changes; that will be the correct train. On the current schedule they depart Locarno at 9:35, 10:35, 11:35 etc. and arrive at Göschenen 93 minutes later. I just checked, and the schedule for October is the same.

Also if your plan is to take the Glacier Express rather than a regular regional train, check the website to check what is required in terms of seat reservations.

https://www.glacierexpress.ch/en/

Whether do this, or noose the other route via the Centovalli Railway, I suggest you take that night from Zermatt and spend it in Locarno instead of adding it to Menaggio. Locarno is a lovely city right on Lago Maggiore, and there are several lakeside hotels just blocks from the train station. This will make you next day’s journey to Zermatt much easier.

Thank you again for the help, I have already made some changes due to your suggestions and tapped on to all the different links you have offered. I've read about the Treno Gottardo and will probably take that train. We had planned on taking the train out of Tirano to Varenna and then boat across to Menaggio. One more question - what is the average weather temp in October?