The distance between Vilnius and Nida is about 360 km one way and it takes at least 4.5 hours. So while theoretically possible, we would never recommend visiting Nida as a day trip from Vilnius. And while Kaunas is 100km closer, it's still not a good idea to drive that far for a day. You can, however, easily visit Nida as a day trip from Klaipeda.