Rāznas National Park (50km east) — Latvia's second-largest national park, centred on Rāznas Lake with its excellent swimming, kayaking, and birdwatching. The surrounding forests and wetlands support a rich variety of wildlife. Easy to visit by car; aim for a full day.
Aglona Basilica (45km east) — the most important Catholic pilgrimage site in Latvia, a grand neo-baroque basilica that draws tens of thousands of pilgrims on the Feast of the Assumption (15 August). The basilica and its lakeside setting are impressive even outside the pilgrimage season. Deeply important to the largely Catholic Latgale region.
Krāslava (30km southeast) — a small town on the Daugava River with a restored 18th-century manor house and a stretch of rapids that's popular with canoeists. A pleasant half-day from Daugavpils.
Vilnius, Lithuania (2.5 hours south by car) — one of Europe's finest old towns, a UNESCO World Heritage baroque cityscape, with an excellent restaurant and café scene. An easy cross-border excursion, and a striking contrast to post-industrial Daugavpils.