Hoi An is not a huge party town as the local authorities keep a fairly strict lid on late-night revelry; backstreets can be very dark after 10pm. The Old Town is a great place to treat yourself to a cocktail or glass of wine.
An Hoi, across the river from the Old Town, offers more raucous action. Happy hours keep costs down considerably, and most places close around 1am. The most popular spots in An Hoi change on a regular basis. Turn right after crossing the bridge from Hoi An, and you'll soon see (and hear) where the backpacker action is currently happening along Ð Nguyen Phuc Chu.