Well, I'm from Syracuse and was stationed there from 2000-2003. I went back to the Watertown area to see how it's changed and it actually has expanded in terms of restaurants and stores from when I was there.
As for boots, I would think the Shoe Dept. store, a sporting goods store like Champs, Olympia Sports or something like that would have some. Depending on what type of boots you want, try a ski shop too, if there any that I remember seeing there.
As far as restaurants, I know there was a Chinese restaurant outside of the gate off of Route 11, but I'm not sure if they deliver. Not sure if the Pizza Hut in that same area does either. Jreck Subs is also in that same area, but they don't deliver. Some of the restaurants in maybe in Black River, Evans Mills, Watertown or Great Bend might deliver to the base. I would go to places by Salmon Run Mall on Arsenal Street to eat or a couple of places Downtown like the Crystal. I think there is a place in Great Bend or Black River called the Golden Corral or something like that, that is good too. If you have kids, you might like Friendly's or if you want to go out with the spouse, try Barkeaters in the Mall or the Barracks Inn in picturesque Sackets Harbor. Fairgrounds Inn on Coffeen is another restaurants to check out too.
As far as ice skating, I believe there is a rink at the Watertown Fairgrounds. There is a rink in Alexandria Bay, about 30 minutes north of Ft. Drum. Theresa might have one too. Syracuse has a skating rink in the middle of Downtown in Clinton Square, that you might really like with Christmas Tree and all right there.
Syracuse might also be the place to go to get the boots and winter gear you might want at places like Carousel Center, Shoppingtown and Great Northern Malls too.
Sackets Harbor, Clayton and Alexandria Bay are beautiful communities nearby with some nice things to do and see, especially in the summer. I think there is a comedy club in Sackets Harbor too. Boldt Castle in the 1000 Islands by Alex Bay and Clayton has things going on and there is the Riveredge Resort in that area too.
Here's some info. that you might want to check out:
Official Boldt Castle Web-Site - Home Page
The Riveredge Resort, Alexandria Bay NY, In the Heart of the 1000 Islands
http://www.sacketsharborny.com/
Alexandria Bay Chamber of Commerce
Alexandria Bay, NY
Watertown Fairgrounds Arena Ice Skating Rink - Watertown, NY - Jefferson County
Greater Watertown North Country Chamber of Commerce, Watertown Chamber of Commerce, Watertown New York
Salmon Run Mall
Clinton Square, Armory Square and Downtown Syracuse NY
Clinton Square Ice Skating Rink - Syracuse, NY - Ice Skating Rinks on Waymarking.com
Ice Skating at Clinton Square - The Syracuse Area Outdoor Adventures Club (Camillus, NY) - Meetup.com (there's skating also at Sunnycrest, Burnet and Meacham Parks in the city of Syracuse too)
Crystal Restaurant » TAUNY Register of Very Special Places
Friendly's : Delicious Food, Premium Ice Cream and Magical Moments with Friends and Family
If I can think of anything else, I'll try to get it for you. Hope this helps.