I used to play a LOT of Forgotten Realms games. Almost all of them started in one of two areas: Boareskyr Bridge and near the Vast Swamp between Sembia and Cormyr.
The games in Boareskyr Bridge featured a very strong Western vibe, but instead of six-shooters, the characters had swords. We had one group that ended up being the actual sheriff and deputies of the area. It was a lot of fun, as the region is largely unsettled. Many Zhentarim and Amnish plots were foiled, as well as one halfling in the group becoming an extremely wealthy merchant. There were also a number of demons in the area, thanks to Dragonspear Castle.
The Vast Swamp region is pretty much perfect for adventuring, as well. There's the swamp, the Inner Sea, a monster-infested mountain range, and the borderlands between two countries that didn't always get along with each other (at least in my version of the Realms). It's more than enough stuff to keep a campaign going for years.
Of course, a few games were in the Thay region, just because they were such evil bastards, and a few more were in Waterdeep (especially after the release of the 2nd edition Waterdeep box). But the Bridge and the Vast Swamp still have the best memories for me.