There are not a lot of great loops in that area. We've done a ton of hiking there, but most day trips and overnights. But the time you get ten miles in, you are already pretty close to the other side, and seeing day trippers from that side.
You might look at coming in via the Blue Lakes trail head, and then hiking into Grouse lake. That is a wonderful hike. But that's an in-and-out
And then you could always go in to 4th of July Lake for the first night, and then down into Summit Creek Canyon...and back out along the ridge. That's a LOT of climbing up and down, though.
Maybe the best option would be out of Lake Alpine---to Wheeler lake the first night, the up over the ridge into Underwood Valley, and then back to Alpine. Make sure you take the time to climb out on peak 9115 on the way to Wheeler Lake, which has stunning views.
But all of this seems less than ideal...for my money, I'd look at Carson-Iceberg or Emigrant if I wanted a better loop.
We've got photos and trips logs of a lot of this area on our website: