For that short of a visit definitely don't do First and I wouldn't go to Grindlewald either. If you really want adventure, paragliding from Murren is amazing and way less touristy. Or the Murren via ferrata.
If those things are "too" adventurous for you, some other great options that are closer to where you'll already be...
*e-bike the Lauterbrunnen Valley (rent from Imboden in Lauterbrunnen)
*go up to Murren and take the Allmenhubel funicular up to amazing view point, restaurant and optional North Face hike (multiple mountain huts along the way)
*Schilthorn and on the way back down do the Birg Thrill walk
*Walk from Murren down to Gimmelwald - walk around the various farms to buy local products from their self service fridges
*Schynigge Platte (great easy hikes/walks along the ridge with views of the lakes and valley)
*train to Wengen, cable car up to Mannlichen, do the Panorama Hike (walk) to Kleine Scheidegg
Since you only have 1 full day, make sure you do at least one of the high mountain options to get really epic views (Allmendhubel, Schilthorn or Mannlichen to Kleine Scheidegg). Since you're staying in Murren it makes sense to do things over on that side and not use up precious time going to other places.
If it were me, I'd probably do this...
*Arrive at noon, park in Lauterbrunnen, ebike the Lauterbrunnen Valley (2-3 hours), cable/train up to Murren, check in, walk from Murren down to Gimmelwald, walk through the little village to explore the farms and views, have dinner in Gimmelwald or cable car back up to Murren for dinner.
*Wake up early to go the Schilthorn first thing, stop at the Birg Thrill Walk on the way down. Return to Murren. Ride the funicular up to Allmendhubel and do the North Face hike counterclockwise, ending in Murren. You can stop at mountain huts for lunch. If you aren't up for any amount of hiking/walking, still go up to Allmendhubel to enjoy the views, relaxation platforms and short walks up around there. If for some reason you finish this all early and are still on the lookout for activities, you can go over to Wengen and potentially go up to Mannlichen for alternative views on the other side of the valley.