Southeast of Bern near Interlaken, the town of Grindelwald makes a great base for exploring 500km of trails. In addition, there are over 100km of prepared winter hiking trails, too!
Try the twisting 4,000 feet climb to the summit of Mannlichen Ridge (7,300) for spectacular views over the Lauterbrunnen Valley, or the other 4,000 assault up to Kleine Scheidegg (6,800) (try the Jungfraubaun cog railroad up and hike down) for vistas up to Jungfrau and the north wall of Eiger. Be rewarded by both with lodges at the summits and by wild downhill returns.
To reach this area from Bern, head south on Route A6 and then east on Route A8 into Interlaken. Follow signs south into Grindelwald.
To reach this area by train, plan to take one of the many international connections to Interlaken Ost, which is southwest of Zurich or southeast of Bern. From Interlaken Ost, transfer to the local Berner Oberland Bahn railway, which serves both Grindelwald and Lauterbrunnen. Once in either of those towns, there are a variety of Post Buses, trams and cog railways to get you to your final destination. If you are flying into Switzerland and planning to take the train, you may want to look into the Swiss Transfer Ticket (swisstravelsystem.ch) that is an inexpensive way to get round-trip from the airport to one ski area.