First of all have a look at http://www.myswitzerland.com/en and the many links you will find there.
Weather: everything is possible, sun, rain, wind, thunderstorms. If weather is bad in Northern Switzerland, it is often fine in the Southern part of the country (cantons of Ticino and Southern Graubunden) and vice versa. Valais is always drier and often warmer than the other parts of the country.
Skiing will only be possible at Verbier/Nendaz (until April 26th only), Zermatt, Saas Fee and Engelberg/Titlis. At the other places in the mountains, the ski season ends between April 12th and April 19th (earlier, if there is no more snow).
Hiking will be fine up to about 1500 metres.
Except some expensive resort hotels, some luxury shops and some minor cableways, everything will be open: hotels, restaurants, shops, post offices, banks, bus and railway lines, etc. However, some mountain railways will have a reduced timetable. So the Zermatt - Gornergrat (3500m) railway will run only once per hour.
The must sees depens upon your interests.
What do you want to visit:
Historical museums, art museums, watch museums, transport museum, ethnographic museums, red cross museum, olympic museum, medieaval towns (with and without citywall walks), medieval castles, baroque churches and monasteries, roman theatres, celtic lake dwellings, menhirs, modern buildings (Mario Botta, Calatrava, Jean Nouvel, Herzog&Demeuron, Diener&Diener, etc.), lakes with historic steamboats, underground lakes and waterfalls, summer ski areas, the highest wineyard of Europe, the highest village of Europe, the longest glacier of Europe, the steepest (highest gradiant) cog railway and cable car lines of Europe, the highest cableway station of Europe (4800 m), Islands with palm trees and tropical plants (Brissago), scenic mountain railways, concerts, theatres .....
SCENIC SWISS RAILWAYS
Almost every railway ligne through Switzerland is scenic. Here are the best ones(in this order of priority):
Glacier Express Zermatt-Brig-Chur-St. Moritz, Bernina-Express St. Moritz-Tirano,
Golden Pass Montreux-Gstaad-Spiez-Interlaken-Lucerne, Voralpen Express Lucerne-Rapperswil-St. Gallen
Old Loetschberg line Berne-Spiez-Kandersteg-Brig, Simplon line Brig-Domodossola-Arona, Centovalli line Domodossola-Locarno,
Gotthard railway Lucerne-Airolo-Lugano-Chiasso,
Mont-Blanc-Express Martigny-Chamonix-St-Gervais (-Geneva).
You find all timtables under http://www.sbb.ch/en/
