Bellinzona — 25 km north by train (around 20 minutes), Bellinzona is Switzerland's most impressive medieval town. Three fortified castles — Castelgrande, Montebello, and Sasso Corbaro — dominate the hilltops above the old town, collectively designated a UNESCO World Heritage Site. The Saturday market is one of the best in Ticino, and the local wines are worth seeking out.
Gandria — A tiny lakeside fishing village accessible only by boat or on foot (no cars), clinging to the hillside above the eastern shore of Lake Lugano. Regular boat services run from the Lugano quayside. The village has a handful of restaurants, narrow stepped lanes, and a genuinely unhurried atmosphere. An easy and rewarding half-day trip.
Como, Italy — Around 30–45 minutes by train via Chiasso and the Italian border. The lakefront town of Como has a beautiful promenade, a handsome cathedral, and the silk-making tradition for which the region is famous. The town itself is often overlooked in favour of the lake, but it rewards a few hours of exploration. Note that you'll need a valid passport or ID for the border crossing.
Locarno — 45 minutes by train, Locarno is Ticino's other major lake town, sitting at the northern end of Lake Maggiore. The Piazza Grande is one of the most elegant squares in Switzerland, and the town's film festival in August is internationally renowned. The nearby village of Ascona, with its artists' colony history and lakefront setting, is a short bus ride away.