Head to Mürrren. Book a room at Hotel Eiger ( close to the train station), Hotel Bellevue ( my choice, it is a longer walk through town but has wonderful views of the Jungfrau massif across the valley), or Hotel Alpina (perched on the edge of the cliff).
For a nice hike, hike up or ride the funicular to Allmendhubel and follow the signs for the North Face Trail, which does a nice loop out to the right (as you face the view), along a ridge with signs telling the history of first ascents on the peaks opposite. There are various choices as you loop back toward Mürren, visiting the little waterfall and/or Gimmelwald on the way.
Next day, take your luggage down to Lauterbrunnen and store it in the lockers at the station. Ride the train up to Wengen, and take the cablecar up to Männlichen. Walk along the ridge to Kleine Scheidegg, with views of the Eiger and Jungfrau in front of you, and the Grindelwald Valley to the left. Have lunch on the terrace at the mountain restaurant on your left before you get to Kleine Scheidegg.
If you long to see the Jungfraujoch/Top of Europe, this is your chance; you buy tickets and board the train at Kleine Scheidegg. ( Personally I feel this popular excursion is overpriced, overcrowded, and overrated, but that is just my opinion.). Or you could ride the train down to Grindelwald and walk through town to the First gondola. It will take you up to the trailhead for a short but beautiful walk to the famous Bachalpsee, which (if the waters are calm) will reflect images of the peaks opposite. Here is a description of the hike, with photos:
You can return to Lauterbrunnen to collect your luggage by train through the valleys instead of over the ridge. Riding all these trains and lifts will not be cheap, but it will be a very memorable day.