Better the weekend of the September 28/30 or the weekend of the October 5/7 for see the best colours of the Fall Foliage ?

Probably the first weekend in October.

October

There will likely not be much color at all in September, unless you head up north to the mountains. The foliage is usually near peak around Columbus Day Weekend in the Boston area.

You just never know, but I'd go with October 5/7, and not Columbus Day weekend, which may be too late. Sept 28/30 is usually a bit early.

Agreed, Oct 5/7, but even then, Boston area is very much secondary to the Berkshires (western MA), southern VT or NH. Absolute peak for the Berkshires is normally around Oct 10 and slightly earlier for southern Vt, NH. Boston follows a bit later and coloring isn't as brilliant along the coast as it is at higher elevations.

Best foliage is either north of Boston (New Hampshire/Vermont/Maine) or west (Berkshires). Unfortunately it can be tricky to assert when THE BEST time to see the foliage at peak color. It can vary --- GENERALLY, the 1st week of October is best. But it can be either earlier or later (you'll get that "shoulda been here LAST week"). And it does matter if you're planning to be in the northern parts of New England versus the area immediately around Boston.

If you haven't bought your airfare yet, you also may consider flying into Manchester, New Hampshire --- driving around NH and Vermont, then head south to Boston & depart from there. Or even consider avoiding Logan Airport altogether --- it can be a bit of a challenge for the uninitiated.