Definitely, hit the museum. Good selection of old warbirds up there.
Depending which terminal you are in, you can get a decent view. From terminal 2, you can look out across to T1, the taxiways, and a few of the runways (been a while, so I forgot which one).
From the left side of T2, you can look out at the other set of runways, if I remember correctly.
Not much in the way of shopping there, so just sit down, and enjoy watching the birds go by.
Might get lucky, the CT ANG has been doing lots of flights recently with their A-10s. Lil old, but still nice to see them. I've seen them 2 times in the last 3 weeks or so, in sporadic spotting that I do from my college (I go to Central CT State U, which is right underneath one of the approaches, but yet again, I am unsure as to which ones)
Also, depending on your approach in, you should be able to see the demolition of Renschlar Field in East Hartford, what used to be the home airfield of P&W, which you being an aviation nut like the rest of us, should be a nice sight. But they are tearing out the field there and putting in a football stadium...