I've been through Bridgeport a few times, and it's always a treat to drive through. The Sierra and the Sawtooth Ridge to the sw are beautiful. My family camped at Twin Lakes when I was a kid (lots of people fish there), and we hiked a lot of the surrounding places. Not many trails, though.
I also once made a x-country week long backpack from Twin Lakes to Matterhorn Pk, and finished at Tuolumne Meadows. (First experience with AMS!) That was a great trip, but it mostly was cross-country off trail.
I have NOT hiked the trails out of the upper end of Twin Lakes,
(map) but it looks like the hike up to Peeler Lake would be good, with a nice loop trail around Crown Point. It crosses into the northern reaches of Yosemite National Park.
While you are looking around, check out the
Green Lakes trail head, the next canyon S of Bridgeport. I've never been there, but the number of lakes makes that trail look quite inviting.
