It is very possible to go from Interlaken to the Jungfraujoch and back in a day. You can take a train from Interlaken to Grindelwald or to Lauterbrunnen then switch to the train for Kleine Scheidegg then switch to the famous 'tunnel' train to the Jungfraujoch. The entire trip takes about 2 hrs (one way).
Many people prefer to stay in Lauterbrunnen to be more 'inside' the Alps rather than looking at them from Interlaken. Personally I find the views from Interlaken to be quite beautiful as well. Staying in Lauterbrunnen also saves you the travel time from Interlaken to Lauterbrunnen (25 min or so) when you travel to either the Schilthorn cable cars at nearby Stechelberg or to Kleine Scheidegg to access the Jungfraujoch.
One caveat, the weather moves quickly in the Alps - where ever you decide to stay - check the webcams and the forecast for your destination before starting. One day the Schilthorn might have open skies and the Jungfraujoch be totally clouded over and the next day the opposite might be true.
Have fun!
-bruce