From Tokyo Station, Odawara is 35 min on the Tokaido Shinkansen, or 100 min on the ordinary Tokaido Line.
From Shinjuku, it's 120 min on the Odakyu Line, which takes its name from the city — Odakyu being short for Odawara Kyukō, or "Odawara Express".
From Hakone, take the Hakone Tōzan Line.
The local speciality is kamaboko (かまぼこ), a type of sausage-shaped smooth, dense, white fish cake. The taste is mild (some might say non-existent), but Odawara's kamaboko is often decorated with a pink cherry blossom pattern on the inside and a slice looks pretty enough floating in a bowl of soup.