Brig , officially Brig-Glis (French: Brigue-Glis, Italian: Briga-Glis), is a city in Valais in Switzerland. The town is nice, though without major sights, but has good connections to Italy, mountain passes, and mountain resorts nearby.
You can fly to Geneva and take a train to Brig (3 hour direct train from Geneva Airport to Brig).
It is an ideal base to go for Glacier Express. Zermatt is 1 hr by train while Italy is 30 minutes away by train (Domodossola). Being close to Italy also means that there is sufficient supply of nice pizza here.
Bike, ☎ +41 79 127 50 17, . Located near the railway station. A bike can be rented for free for 4 hours with a deposit of 20 francs. Wednesday to Sunday, 9 am - 12.15 pm and 1 pm - 6 pm from June to October. edit
Take a stroll in the town centre. Typical Swiss town, with a nice river passing through the town centre.
Take a local bus up to the Simplon for lunch, have a swim in the lake or go for a hike among 3500m above sea level+ peaks.
Take a 5 minute train ride to a small town called Morel. Take the cable car up to the Riederalp. From here you have access to one of Europes best ski resorts, unknown to most non-Europeans, named Aletsch. $700 full season ski pass.
Europe Hotel  right in front of the train station. CHF140 per night.