
Atami is on the Tokaido Shinkansen, which makes it the fastest beach-onsen escape from Tokyo - about 50 minutes, no transfer. There's also a slower, cheaper local route if you're not in a hurry. The station sits right above the town, so you're soaking within minutes of arriving.
For a day trip, yes - the Shinkansen nearly halves the journey and leaves more time to soak. If you're counting yen or have a Japan Rail Pass that covers the local line, the slower train is fine and still direct. Tap an IC card for the local; buy a Shinkansen ticket at the gate or machine.
Take the Tokaido Shinkansen from Tokyo Station - about 50 minutes, ~¥3,700, no transfer. The JR Tokaido local line is cheaper (~¥1,980) but takes 90-100 minutes.
For a day trip, yes - it nearly halves the travel time, leaving more time to soak. If budget matters or you have a rail pass, the slower direct local train works too.