There is a list of area hotels on the Parent's Association web site that honor the "Coast Guard Academy" discount, just let them know you are staying in conjunction with the CGA and you will be able to get the rate, no "proof" will be required. Ask when you book the room.
The academy is an "open" campus, all that is need to enter is a valid ID (driver's license). The buildings, however, are not all open, and you will not be able to enter some of them without a cadet escort or in some cases not at all (i.e. Chase Hall, where the cadets/swabs/AIMsters live) is not usually open to visitors except on special occasions. On Friday, Billard Hall is where the Engineering Competition will take place, you can come and go as you please and observe your AIMster as they compete in the challenge. Their "graduation" will be in Dimick Hall (all the way on the other side of the campus, bring comfortable shoes).
The museum is located in Waesche Hall, the same building that houses Admissions and the library (lol) and that building is always open for visitors. It's not very big, you could probably see everything in the museum in less than an hour. Up on The Hill (where the Superintendent and Commandant live) is the Hopley Yeaton memorial and the Chapel, both worth taking a look at, and the sailing center down at the waterfront (Jacobs Rock) is also a nice place to get some great waterfront pictures.
As for the town of New London.......go visit Mystic, Providence, or Boston.