I've been going to this museum since I was a little kid. I'm still able to enjoy a visit today.
Half the museum is targeted towards kids with mineral science and local history. Not to worry, there is plenty to enjoy as an adult in this section. This part of the museum is permanent and has not changed much since the museum renovated a while back.
The second half (literally, it's the left side) houses temporary collections with most of the pieces on loan from other institutions. It can be a hit or miss since artwork is extremely subjective but I have never seen anything really controversial without a sign in front if it's remotly so. (Don't worry parents.)
For people who live near Greenwich, it's a nice place to spend the afternoon without the hassle of going down to the city (NYC).