If you thought that Narva’s central-city border crossing was odd, wait until you see Valga. This town was the only place that was seriously contended between Estonia and Latvia after WWI. A British mediator had to be called in to settle the dispute and suggested the current border, splitting the town in two. As a result, as you wander around the town centre you’ll find yourself passing in and out of Valga and Valka (as the Latvian side is known). Mercifully there are no longer checkpoints (cheers, Schengen!), although you should really carry your passport with you. The local authorities co-operate on important stuff like tourist information and bus services.
Valga is enjoying a slow process of gentrification, but its old wooden houses and parks are still skirted by some grim industrial areas. Its bloody wartime history makes it an interesting place for a brief stop before moving on. Although there are some large military bunkers and war cemeteries on the Valka side, most items of interest are on the Estonian side of the border.