I don't really think that Refrigerator Gulch would be a good base location for day hikes. There's nothing close by. Personally, I wouldn't want to camp there, either, although plenty of people do when making the loop. I think of it as the buggiest spot in LCW. Anything you do in that area is going to be off trail and a lot of work. No significant peaks nearby. The area isn't even mentioned in the LCW Classic Summit Hikes book. There are plenty of rock formations to explore. If you're set on the base camp/day hike thing accessing peaks, I'd look at other areas. If you start on the southwest side on Brookside-McCurdy or Lizard Rock trails, you could camp at McCurdy Park and then do day hikes to McCurdy and Bison peaks.
Is it that your friends don't feel like doing the loop or don't think they can? If they can make it to Refrigerator Gulch in one day, they should be able to complete the loop. There's a tough climb out of RG to McCurdy Park but then if you take the trail through Lake Park, it's not too bad of a climb then it's all downhill back to the TH.