When we were on the BI last summer we stayed 2 nights at the Volcano Hotel and then drove on to Kona. We spent the first day at the Volcano park and then the 2nd day we took the long route to Kona (north route) and spent the day sightseeing on the way to Kona. We flew into Hilo (45 min. from the park) and flew out of Kona to do this conveniently.
It's 90 miles and about 2.5 hours one way the short way (south from Kona) -
map
One thing to consider is that if you plan to hike out to the lava, the drive to the trail head and hike to the lava flow could be a 4-5 hour round-trip or more, and you will still want to see the rest of the park. Also - the lava is not always flowing and not always accessible, so check right before you go.
Park website It certainly could be done as a day-trip, but it would be a long day, and tiring if you hike out the the lava flow and then have to drive back 2.5 hours in the dark.
It would be fun to spend the night. There is actually a hotel in the park with a view of the crater that would put you right in the middle of things.
Volcano House
If you want something less expensive, but still in the park, you could stay at the
Kilauea Military Camp (rustic resort for military and retired military and their families) if you have someone in the military who can make the Resv. for you.
There are also accommodation in nearby Volcano Village - but for one night, I would stay in the park.