The OP was asking about the weekend just gone by, so I assume the question applies to a wet, cloudy day this month. I would avoid anything with a water crossing right now, or bring extra foot wear to prepare for completely soaking your feet to cross. Water is at or above record highs just about everywhere in the region this year. Here is my report from yesterday attempting to get to Bigelow/Sugarloaf (Maine).
http://www.vftt.org/forums/showthread.php?t=40464
( I was not sure where to put that so I put it in the trail conditions section).
In more typical conditions, if I want to summit something on a cloudy or showery day, I go to places
1.) closest to home (no need to drive all the way to New Hampshire for me to look at the inside of a cloud, it looks the same from Camel's Hump which is much closer to me) (I avoid Mansfield in the rain, something about Green Mountain rock is much slicker then White Mountain or Adirondack rock, and Mansfield has allot of exposed rock).
2.) A peak where I have seen the view before so I do not miss anything new
3.) A peak that follows a brook, the brooks are worth the price of admission themselves some days.
4.) A tree mountain with limited distant views anyway like Cabot, Waumbek, et al
This time of year I also looking to avoid snow as much as possible so I also look for southern slopes.
Yesterday I wound up going up Waumbek since it met all of my criteria and happened to be most convenient for me as well.
If it is pouring rain for the whole day based on forecast I just do not hike. If it is just showery (like yesterday) it can be worth going. Sometimes you can steal the prettiest views on wet days. The mountains north of Waumbek had the smokey mountain look yesterday, as New Hampshire was in a relatively dry patch of weather yesterday afternoon. The sun did not come out, but at one point I could see my shadow (it was trying), and it stayed dry for my entire hike.
One other note, I drove my the Appalachia TH yesterday and zero, 0, no cars (vehicles of any kind) there. I can't recall ever seeing that before, I regret not taking a picture, so you will just have to take my word for it. Lots of great water fall hikes & loops from there on a rainy day.