Sorry, I thought I read August. Must have been another thread.
The benefit of camping at Horseshoe Meadows (about 30 minutes away from the Portal) is the 10K' elevation, about 1500 feet higher than the Portal. This will help acclimation a little better, but you then give up the convenience of having the Portal Store close by those two days before the hike. The other caveat is that HM technically has a one-night limit. This rule is broken all the time, but you never know when it might be enforced. Then there's the drive to the Portal to start the hike - adds another half hour-plus to that super-early wake-up on Day One of the hike.
If you're taking Diamox to aid acclimation, staying at the Portal shouldn't make that much difference versus HM, especially since you'll have 3 nights sleeping at elevation before going above 12K'. If you just had one night to acclimate before heading up I'd say use HM, but two nights at the Portal and one at 12K' would work for me.
And yes, TC will not be nearly as bad in June as later in the summer.