Thumbs up
Since I lived in the area I never stayed at the Claremont myself but I have put friends and family up there and can tell you that although somewhat pricey, it is a first rate hotel. You will not be disappointed if you stay there. The Claremont is about 15-20 minutes from the academy. The only more up-scale hotel in the area would be the Garden City Hotel which is a little further away.
FYI ... there are a number of really good restaurants on Northern Blvd.
(NY25A) between Great Neck and Roslyn including such top steak Houses as Peter Lugers (cash only), Mortons and Bryant & Cooper (in Roslyn).