On day 2 skip Bern and explore Luzern instead. Makes no sense to split your limited time. In the end you'll only have scratched the surface of both cities.

Lugano makes a good base for exploring the other lakes, too. You can easily hop on a bus to Menaggio (Lake Como) from where you can take a ferry to Bellagio. Or go by train to Locarno and hop on a ferry for exploring Lake Maggiore. However, I would spend some more time at Lake Lugano once you're there - the smaller villages are the best. Gandria, Carona, Morcote ... lake cruise, funiculars, walking.

www.bellagio.info my fav makes a perfect base
For 12 euro take a shuttle to Menaggio from Lugan
then ferry 5 minutes across. It is the pearl of
Como hotelflorencebellagio.it nice.

Stresa/Baveno/Isola Bella best base for Magiore
Hotel Grand Dino or Regina Palace my fav www.booking.com
gooddeals usually.

Have done car with europcar.com expensive more convenient.
A great way to circumnavigate the lakes. train seat61.com
cheaper but more circuitous but quite doable.

A beautiful area otherwise looks fine Have fun!

I'd do Titlis and Engleberg rather than Pilatis

I would get a car in Lugano and spend 3 nites at one lake destinations--and reutrn the car in Lugano and train back to Zurich. I suggest staying in Stresa for that time and seeing Lago Orta as a day trip. Drive ot Stresa via Locarno and down the west shore. Stop to see the gardens at Villa Taranto near Verbania. Have fun.

Thak you all for this priceless information. It seems that there are many in this forum recommend Berner Oberland region. Am I missing by not venturing in this area? If yes, what can I change?
Also for the lake region, Is Stressa a good base for lake Commo as well as for lake Maggiore?
In May Swiss pass offers 2for1 deal on a 4 day pass. Do you think it is worth buying 2X4 day pass pp instead of renting a car.
Thank you all again,
PK

Your problem is not enough time.
If you find 3 more days then think about the BO and Lago Como.

Bobthenavigator, do you think swapping Bern for OB worth it?
From Luzern we will take a William Tell express to Lugano. Is there a another path we can take from Lugano to Zurich?
THanks, PK

Do you have to go back to Zurich? If you've already bought your plane tickets, could you change them for not too much money? With this itinerary, flying out of Milan makes more sense. And you'd save the money and time spent backtracking.

Mimar,
You are absolutely correct. We are going to Karlovy Vary via Prague after the trip. I could not find reasonably priced tikets, from Milan to Prague. From Zurich rt to Prague air is $280. So we just bought rt tickets Phila to Zurich.