Alternative High Peaks base camps to Marcy Dam, Lake Colden, Flowed Lands

Hi all!

My first time in the forum and planning my first overnight trip. I've been hiking in the Adirondacks, Greens, and Whites for years but never overnighted.

My plan(conditions permitting) is to hike in to the interior Sunday afternoon 6/20 setting up camp for a couple nights at Marcy Dam or Lake Colden and doing an Algonquin, Iroquois and Wright loop one day and Colden another with some exploring in between.

Questions are:

Will I have trouble finding a tent site?

Is there another similar area with tent sites surrounded by peaks?

Would it be better to come from AdkLoj due to mud/bugs over Upperworks this time of year?

And I'd appreciate any tips on lower elevation trips as a backup plan if that's what happens.

Thanks for any and all insights!!
(I've read all camping regs and trying to educate myself as best as possible)