time tends to be early-to-late June depending on the altitude & species.
I have reliably seen Diapensia in bloom in the southern Presidentials in mid-late June, alpine azalea about that time and mountain avens (Geum peckii) then also, Lapland rosebay is supposed to be in bloom slightly earlier, I think.
Any trip to the Alpine Garden in mid-june should be a reliable hike though if its on a weekend I would imagine it would be relatively crowded, esp. since it's probably the closest alpine habitat to a paved road.
Put on your google hat and look for the Maine mountains above treeline, there are a handful (most in Baxter Park, much of the rest in the Stratton area). There is some public information about what species are where, it tends to be more obscure to locate & will only tell you which township. I have not personally been wildflower-hunting in Maine yet so can't advise.