See the map with the blue arrows, I've been to all of them with Lake Cochichewick being my favorite to shore fish in that area.
I don't know of any shore fishing with "access" directly in Methuen, and by access I mean having not only space to fish from, but also not infringing on private property.
*Late edit: Just read your post , not the heading, Lawrence is probably your best bet to fish the Merrimack. There was talk of the ramp in Methuen being repaired, but I haven't seen anything. The entire stretch of the river that goes through Methuen (along 110) is nearly impossible to shore fish from.