Where to visit on 2-3 week trip?

Switzerland is a terrific destination, land in Zurich and take train straight to Lucerne, enjoy the river by ferry hike in Mt Pilatus or Mt Rigi (a day spa is also avail at reasonable cost) then to berner oberland area. Stay in lauterbrunnen valley there and see by gondola the mtns, hiking, waterfalls etc. reserve your lodging soon as these areas are very popular. You could Also land in Geneva then go to Laussane to enjoy the lake and its sights, and historic paddlewheel ferry to,Montreux. Then make your way by train to berner oberland and Lucerne. Train south to dolomites or to venice.
The Italian dolomites are beautiful and a hikers dream but to me not like switzerland and not as easy to get around. I stay in hotels so cannot comment on apt rentals.

Costs in the Dolomites were very reasonable for me in July 2015. I'm sure, based on comments on this forum and elsewhere, that costs in Switzerland are much higher. You can check this out yourself by looking at lodging rates on booking.com. Compare Ortisei (mountain village in the Dolomites) with similar places in Switzerland like Muerren and Wengen. Also compare the valley town of Bolzano to Lucerne.

Switzerland is comparatively light on museums. The Transport Museum in Lucerne is popular, and I believe there's an art museum in Basel. You should travel with a good Swiss guide book, and that will be your best source for museum info. Just check current hours online before finalizing your itinerary.

Since you have a good bit of time, I'll mention that I enjoyed Appenzell. It's dairy country, not high mountains. The town is very pretty, and the cute little local train felt like a bus on wheels.

Especially if you ultimately decide not to include Italy on this trip, you should consider a few days in the Ticino, the Italian-speaking part of Switzerland. Although I prefer the lively city of Lugano, the more staid Locarno is a great base for some interesting side trips. I've taken the Postbus up the Valle Verzasca a couple of times (don't expect much water in the mini-waterfalls in August), and the Centovalli railroad line to Domodossala, Italy, is very interesting.

You might Google "best European rail journeys" or the equivalent and do some reading. You'll find several Swiss trains listed. The buses that start at rail stations and run up valleys (like the previously mentioned Valle Verzasca) will get you into some less touristy areas.

You'll want to take at least one boat ride on a Swiss lake. This is my advice: Do not assume that, because 1 or 2 hours on a lake is good, 4 or 6 or 8 hours is better. However beautiful, spending half a day or more on a lake, just looking at the shore, gets repetitive.

I agree with JS, above. Having spent many summers in the Lauterbrunnen region, both when my kids were teens, and then as college age, I can respond to the Swiss aspect of your trip.
You said you wanted scenery, trains, lifts, and hiking distances of 5-6 miles? You got it! (Throw in cows, goats, and sheep for free!) All but one of the hikes below are around 2 hrs.
We typically aim for 10 days in the Berner Oberland region, realizing that rain, fog, overcast will affect perhaps a third of the days, leaving maybe 6-7 good hiking days. Here are our favorite hikes and some maps:

1. Mannlichen to Kleine Scheidegg (and even further to Wengernalp). Train back to Wengen. This is the BEST hike for a clear day.
2. Grutschalp to Murren, pretty much parallels the train tracks.
3. Top of Almendhubel, go right, generally heading above Winteregg, then clockwise back down to Murren
4. Top of Almendhubel, go left, towards Schiltalp, then Spielbodenalp, then to Murren
5. Murren to Sprutz Falls, under the falls, up the opposite side to Spielbodenalp, then back to Murren
6. Lauterbrunnen to Trummelbach Falls. Enjoy the falls and the walk through the valley
7. Schynige Platte to First (6 hrs, but great! Get to First before supper, when cable car closes.)
8. First to Bachalpsee and return (shorter version of #7)
9. First to Grosse Scheidegg and bus back to Grindelwald
10. Grindelwald, cable car to Pfingstegg (take the Rodelbahn luge ride there!), hike to Berghaus Baregg (If it rains, there is the Lauterbrunnen museum, Trummelbach Falls inside the mountain, eating, shopping the huge Coop in Interlaken Ost.)

Maps:
https://terrelledwards.files.wordpress.com/2012/01/hikingmap1-3-2.jpg

http://ontheworldmap.com/switzerland/ski/jungfrau/jungfrau-summer-map.jpg

http://www.pfingstegg.ch/index.php/en/timetable-prices-4/wanderkarte

Shoe gave great recommendations for hikes on the good-view days. For the foggy/poor view days, besides the must-see Trummelbach Falls and shopping that Shoe recommended, here are mine for the foggy/poor view days:
Visit castles: Thun Castle, Oberhofen Castle (near Thun), Chillon Castle (near Montreux), Gruyères Castle.
(Thun Castle hosts concerts inside, some nights.) Visit the ramparts and ancient clock tower in the Luzern town wall.
Visit museums: Ballenberg Museum (near Brienz), Einstein Museum (in Bern), Chaplin's World (near Vevey), Transportation Museum (in Luzern), Paul Klee Museum (in Bern), Rosengart Museum (in Luzern)
Visit (very) old parts of towns: Luzern, Bern, Brienz, Gruyères, Thun
Don't miss the plazas with murals on the ancient buildings in Old Town Luzern and, in the newer part of town, the weeping lion monument;
Watch the bears play in their renovated bear park in Bern.
Brienz has an unusual shop with jewelry made from pressed Swiss flowers.
Gstaad has very charming decorated old buildings.
Walk the river-gorge cliff-walk at the Aareschlucht near Meiringen (take the train there), or walk through the Rosenlauischlucht (Rosenlaui Gorge) near Grosse Scheidegg (take the bus there)
Walk along and behind Giessbach Falls (Get there by ship from Brienz to Giessbach.)
Ride the very scenic train from Luzern to Montreux via the Brunig Pass, Brienz, Interlaken, Zwiesimmen, Gstaad.

The others already have mentioned many of the things I'd have recommended, but here are my thoughts anyway.

Frankfurt is an awfully long way from Switzerland and depending on what places you want to stay at it's even further. If you do however decide to fly in there I strongly suggest you consider a short detour along the rhine gorge between Koblenz and Bingen.

My suggestions for hubs are: Lauterbrunnen valley/Interlaken, Lucerne/Lake Lucerne area, Appenzell and maybe Chur/Flims.

Chur would also be a good starting point for the Bernina Express down to Italy. Another interesting though more complex train trip would be the Glacier Express to Andermatt, optionally a roundtrip on the restored steam train over the Furka, then either directly down to Airolo->Bellinzona o down to Erstfeld then through the base tunnel.

As another has mentioned. Should you decide to not go to italy then Ticino is highly recommended as an additional stay.

Thank you so much all the information! I am researching as fast as I can to try and decide. Right now the fly into Frankfurt is because we can get it non stop but will look into other options. (Train tickets appear to be about 100 each and that is about the price to add the additional flight to Zurich) I was going to take the train to Lucerne the next day.

-5 nights Lucerne
-5 nights Berner Oberland ( all the info on hikes was so helpful, I might even add more time)
-one night Zermatt (seeing the Matterhorn is not top of the list, but this is where the train starts) for the Glacier express train
-one night at end of glacier express then Bernina Express to Tirano and then change to regional train and get off at Varenna

My husband is considering going back to Salzburg because the three days we were there (12 years ago) it was raining (the hills were definitely not alive) and he wants to see that area with the mountains visible, again may not work. So Lake Como, (maybe Venice) and then Salzburg-all appears to be quite doable with trains. (12 years ago my brother was working in Germany and we were able to use his car and do a quite a bit a bit of traveling in Germany, France and Belgium.)

I have a couple more nights to decide on. Is it worth it to go all the way to Zermatt for the whole glacier express train? Still pondering Appenzell and Gruyeres/Montreux.

flight to Zurich) I was going to take the train to Lucerne the next day.

Just so you know, there are direct, hourly trains from the Zurich airport to the heart of Lucerne, and they only take an hour (leaving 47 minutes after each hour). There are also other trains between them (18 minutes after each hour), but you'd have to change trains once on those. The web site for the Swiss transportation system is www.sbb.ch/en.

This is just a guess, but Zurich is a major, major business center. Even though Lucerne gets a lot of tourist traffic, hotels may be less expensive there. It's generally considered a more attractive place for tourists to stay, so unless you have specific plans in Zurich you might just go on to Lucerne on arrival day. That means one less hotel change.

I like acraven's idea about first night staying in Lucerne.
I'm wondering if you really want 5 nights in Lucerne. You can explore most of the town sights in a day (Kapell bridge, Lion monument, glacier garden and mirror maze next to it, etc). Then there are the mountains Pilatus and Rigi. To me, that's 3 days, and I'd put the extra 2 days into Lauterbrunnen/Grindelwald area.

You said your husband likes scenery. You can both Google Image the Lucerne sights above, and then compare them to what you see when you Google Image:
Lauterbrunnen, Murren, Bachalpsee, Grosse Scheidegg, Trummelbach Falls (all within a 5 min radius).

As for museums, I would combine a visit to the Appenzell region with a must-see visit to one of the oldest libraries in Europe in St Gallen (Abbey Library or in German, Stiftsbibliothek; Google for more info). Appenzell, the town, is tiny and quaint, surrounded by fantastic hiking as well as numerous cable car ascents if you wish (and with small restaurants always on the top of the mountain....). The library is simply a wonderful place, small but full of history.

I would also strongly suggest overnighting at least one night, more if you can do it, at the Hotel Rosenlaui in the Rosenlauital above Meiringen. It is an old hotel, full of history as well, and also surrounded by sheer rock walls and great hiking (and a river runs through it! Well, a creek....). Up the road from this is also the Schwarzwaldalp hotel. Access to these is by foot, car or Postauto. Check their hotel websites.
Kandersteg is also a good locale for hiking and sightseeing, small town, numerous rooms for rent, on the train line.