Gimmelwald is the idyllic, quiet locale popularized by our host, Rick Steves. As such, if you want to stay there 5 weeks from now, you had better secure your lodging NOW.
Lauterbrunnen is in the bottom of a deep, beautiful valley. It will be the least expensive locale, and most convenient for visiting other sites in the area. Only downside would be that it gets less sunlight because of its location, but if you are traveling every day, that might not matter.
Wengen is up on the mountain on the way to the Jungfrau. It is car free, but busier than Muerren, and way busier than Gimmelwald. It is the most convenient spot to go to the Jungfraujoch. Higher prices than Lauterbrunnen.
Zermatt? You can take the Gornergrat train up for a great view of the Matterhorn. You can also take the cableways up to the Klein Matterhorn for a close up view of the Matterhorn, as well as walk inside of a museum carved into the ice of the glacier. That warm jacket will come in handy.