I usually go for a beer as soon as I can. Some of the best drinks I've had at WDW have been the simplest:
1) Having an IPA at the Big River Grille on the Boardwalk a few minutes after checking in on Day 1 of my latest trip. Hot day, cold beer, overlooking the boardwalk and lake over to the Beach and Yacht Clubs, the first of seven days of fun. Perfecto.
2) On a trip several years ago with my wife and girls we had a lunch ADR at Mama Melrose at DHS. It was during the hottest July on record a few years back with a heat index on that particular day of 115 degrees. We stepped into the AC in the entry area and got our table after about 5 minutes and moments after we sat I had a Peroni in a frosty beer mug and almost passed out from the elation.
For booze, it has to be the Diablo from La Cava in the Mexico pavilion in Epcot - or the Margarita kiosk on the Boardwalk and it's gotta be a lime over rocks with a double shot of hot pepper simple syrup.
Never been to Trader Sam's, so I'll have to hit it up next trip. Maybe my new favorite is there.