Clam chowder. With clams, it almost stands as a fish dish, doesn't it? So I recommend you to make something with meat. I will stay away from a cream based sauce because you said you are making New England clam chowder. If it were Manhattan CC, a buttery/creamy sauce for meat would be nice.
Easy comfort dish would be roasted chicken. I think it would be nice to eat roasted chicken and roasted potatoes after or with NECC. This really doesn't take time either. You just put chicken in the oven. Meanwhile, you make clam chowder. Then you serve the soup and (then) chicken.
In terms of flavors, two should go well. Cream, mushroom, chicken and potatoes go well with each other. In this season gradually getting cold, warm soup and roasted chicken sound attractive to me.
I wouldn't put potatoes in the soup if I roast them with a chicken. I would put mushrooms in the soup because it goes well with everything else.