It isn't guaranteed you'll be able to see an active lava flow at (or outside) Hawaii Volcanoes National Park, but if one is active and accessible while you are visiting, it is an unforgettable sight. I was fortunate to see lava flows at night both times I visited in 2010 and 2011, and they were incredible. The Pu'u O'o eruption on the eastern side of Kilauea volcano has been flowing intermittently for over thirty years, crossing park boundaries, destroying housing developments, and nearing the town of Pahoa in 2014. Just west of the town of Pahoa are guides offering night-time hikes to the Pu'u O'o lava flows outside the park, and in 2010 I was able to watch lava flowing into the ocean on one of the tours. Officially the park warns about the dangers of walking out to the lava flows with a guided tour, so it is up to visitors as to whether they want to take the risk. Inside the park you can see the glow of a lava lake active within Kilauea crater, as well as trails traversing former eruptions. The lava lake rose high enough to be visible in April 2015, but has since subsided. Whether or not lava flows are active when you visit, it is pretty awe-inspiring to witness some of the youngest landscapes on earth.
Logistics: The airport in Hilo is the closer airport on Hawaii's Big Island, and the park is a short drive away. Pahoa and the Pu'u O'o flows are east of the park, but are not directly accessible from the park.