Hotel Pollux is a terrific option if you're looking for a reasonably priced hotel right on the main street in Zermatt. It's conveniently located to all the shopping and restaurants. The rooms are very clean, but a little on the small side. Amenities, such as bar, sauna and restaurant are all great. Can even buy your ski tickets at the reception desk. The room was hot (can't control the heat), and our room windows were right on the main street, so we heard people coming home from bars at 2am. Try to get a room on the back side of the hotel.
It's a bit of a hike to the Zermatt gondola, but there is a bus that stops by the river and is about a 5-7 min walk up. The train station is a 3-4 min walk away, as is the train up to Gondergrat. The funicular is about 7-8 min walk as well.