best place to hike in the Swiss Alps

I'd suggest reading the entries under the Switzerland section here on the Forum, along with the Trip Reports. You are fortunate because this has been discussed already in great detail. Review the posts over the past twelve months.
Have a wonderful trip in this beautiful country.

At what level do you hike? Are you “easy-hikers” who enjoy a 2 or 3 hour outing with not too much elevation gain or loss, or are you long-distance go-all-day-no-mountain-is-too-high types?

We found the area around Zermatt to be more challenging than we like (we are easy-hikers) and we very much like Pontresina in the Engadine as well as Kandersteg in the Berner Oberland and Bettmeralp in the Valais, but we spend significant time in Lauterbrunnen each year due to the variety of hiking and vistas we find there that suit our style.

FWIW, we spend at least 4 nights anywhere in the mountains because some times weather does not cooperate. We once spent 3 nights in Chamonix and never saw Mont Blanc, and a few weeks ago in the Lauterbrunnen area there were 5 sequential days of periodic rain and mostly overcast. Luckily we were there for several weeks so got our chance at a lot of good weather, too.

If it were me I would go to Lauterbrunnen and hike from Männlichen to Kleine Scheidegg.

We just spent 4 weeks hiking in the alps of Switzerland, Austria, Germany and the Dolomites in Italy. I have also hiked in 3 of the 4 areas you are thinking of...we were suppose to go to Bergun near Davos this year but an early snow made for a change of plans. We have hiked in the Pontresina area near St. Moritz and enjoyed it very much. Out of the 3 I have hiked, I would rate them:
1.Lauterbrunnen
2. Chamonix
3. Zermatt

If the sun is out in Lauterbrunnen, it is fantastic. We try to spend 5 nights there when we go. You don't say what distance or level of hikes you want, but here are the ones we did this year:

1. We hiked from Mannlichen to Kleine Scheidegg, then rode a train to the Gleischer station and hiked the Eiger Trail. These 2 could be done on different days.

2. We hiked from Gimmelwald to the Obersteinberg hut. This is a more challenging hike and it was our fourth time doing this hike because it is one of our favorites.

3. We hiked the North Face Trail from Murren. Fantastic hike with stunning views. We hiked up to Almendhubel then down to Murren. We did the detour to the Spurtz waterfall.

4. Schyngie Platte to First. Challenging but fantastic hike. If you want shorter ideas for this area, you can do the Panorama hike from Schyngie Platte and ride the train down. Also, taking the lift to First and hiking to the Faulhorn hut is a great hike.

Lifts are expensive in this area. We paid $215 per person for 4 day Jungfrau travel passes that included most of the trains and lifts in this area. (Does not include the Stechelberg lift to Murren and the Schilthorn. Also, doesn't include the train to Jungfrau Joch (but you can go as far as the Gleischer station)

This was our fifth visit to Lauterbrunnen. I did find this web site helpful in looking for new hikes to try:

https://www.earthtrekkers.com/switzerland-travel-guide/

We did some hiking in Chamonix and enjoyed it. However, it does not come in as high on our list of places we would like to return and hike again. The previously mentioned web site has some information on hiking there:

https://www.earthtrekkers.com/destination-france/

They also have a section on hiking in the Zermatt area. I rated this the lowest. However, I have to say that we hiked there in 2001. The internet was not nearly as helpful in planning hikes as it is now and that could have affected my rating. (RS didn't even include it in his book back then) We basically just hiked steeply toward the Matterhorn until we got tired then hiked back. I have never been tempted to go back to Zermatt.

For the record: I have no affiliation with the web site I recommended. Usually when I am planning on hikes on trips, I google "best hikes in "wherever I am going" and get very useful information

Thanks everyone. It seems like most people are in agreement that the Lauterbrunnen area is the best area. It also seems that Jungfrau and MAtterhorn are beautiful to see from other hiking spots, but it isn't worth the money and crowds to go up to them. I have gathered all the information and will start making some final decisions in the next month or so. I really APPRECIATE all the help!

I've not hiked here (yet and when able), but have seen it recommended in these Forums several times. Oeschinensee. We have put the car on the train on the Lötschbergbahn between Bern and Valis several times. Makes for a quick trip between the regions. You can sit in your car for the trip. Come prepared for mountain hiking. Almost reached hypothermia unprepared in freezing rain above Davos years ago.

Once you have chosen a few hikes it will be good to look them up on Switzerland Mobility Here you can see if the hiking trail is a Wanderweg or Bergwanderweg (mountain hiking trail). The Eiger Trail, for example, is a mountain hiking trail.

Here is a description of the things you can expect from each of these different types of trails:

Wanderweg

• Yellow signposts, rhombuses and directional arrows mark the trail
• Hiking trails are mostly wide, but can be narrow and uneven in places
• Steep passages will have steps and areas with danger of falling are secured with railings
• Sturdy shoes with a grippy sole, appropriate clothing for the weather and a map are recommended

Bergwanderweg

• Yellow signposts with a white-red-white tip and white-red-white markings painted on rocks, etc. along the trail
• Mountain trails are mostly steep, narrow and sometimes exposed
• Particularly difficult passages are secured with ropes or chains
• Hikers should not only be sure-footed, vertigo free and physically fit but also familiar with the dangers in the mountains
• Trekking shoes that include the ankle joint to protect it from twisting and equipment adapted to the weather are important, a hiking map is also recommended.

I got this information from the Swiss hiking organization. You can read about it here, they have a lot more information as well as photos of what the different hiking signs look like. You'll need to translate it into English.