Odawara is a castle town on the border of the Tokyo Metropolitan area. It is not really famous, though many people have passed through Odawara in order to reach Hakone. But be sure to give Odawara a visit, as there are plenty of interesting sites to visit as well as many walking routes.
In the below picture you can find an overview of beautiful walking routes starting right from Odawara station.
Maps by openstreetmap.org
An advised route is to start at A and walk to F, go via G to T (Shiroyama 2nd Park), then all the way to V (Odawara Castle Park) and head back via W (Ohoribata Street) to the station. This loop is around 1.5 hours long in case of continuous walking. Considering some rests and enjoying viewpoints, 3 hours is a more reasonable time to schedule. And of course you can expand the route as much as you want by also walking the KLMNOP points. Below the map you can find pictures taken along the routes.
A – Odawara Station West Side 
B – Go up this stairs if you come from station 
C 
D 
E – Coming from B, go to the left here 
F – Coming from E, the left goes to G, the right goes to K 
G 
H 
I 
I 
J 
K 
L 
L 
M 
N 
O 
O 
O 
O 
O 
P 
Q 
R 
S 
T 
T 
T 
V – Odawara Castle Park 
W – Ohoribata Street 
X