Oh so many choices!
Since you are starting midweek, I think that you will be ok with getting a walkup permit, so I would recommend the following as the best route given your criteria...but it will require taking the shuttle from the Valley to Tuolumne either at the beginning or the end of your trip, depending on what works better for you. Start your hike at Tuolumne Meadows, head up the Lyell Fork and then Rafferty Creek to the Vogelsang area, then down to Merced Lake and on down the Merced River to the Valley. Lakes and creek the whole way, along with stunning scenery.
And if that trailhead quota is full you could go for any number of Tuolumne Meadows alternates, like the trip described
here, which is a great hike but does include a bit of off trail hiking...not sure of you are into that.
And if nothing is available there you could continue over Tioga Pass and go into the 20 Lakes Basin. Less of a loop there but plenty of lakes! And back in Yosemite, off of the Tioga road, there is always the Ten Lakes Basin, although some say 20 Lakes is twice as good
If the Bridgeport area is not too far out of the way you could look at a loop into the head of Virginia Canyon, starting at the Green Lakes campground. Or head up to Peeler Lake from the Twin Lakes area.
And if you are coming up from the south you might consider starting just outside the southeast corner of the park...Clover Meadows trailhead into Lillian and Slab lakes vicinity.
Maybe check out those options and more info can certainly be provided if you want.