Bike is the great mode of local transportation for holidaymakers in Orebic. 2,5 km from east to west end of vilage itself is easy stretch of road (or seaside promenade if you preffer it that way) running almost flat (please have in mind that the actual house you may stay in may be a bit up hill from the main street). Nearby Perna (1,5 km), Kuciste (4 km) and Viganj (6 km) can be reached with minimum effort using seaside road with moderate traffic.
Same route is excellent for beginner recreative biking - you can make a circle of about 20 km with minimum elevations, making it great recreative route.
For those more demanding, there are excellent scenic routes to nearby Loviste to the west or Trpanj to the northeast both taking about 20 km in one direction with about 250m elevation. Of course, you can take it further to Ston (57km) or take the bike across to Korcula island and take another 60km of local roads with moderate traffic.
If you preffer trails and paths, you can take your mountain bike trough the vineyards, olive trees and pine forest on Sv. Ilija, following walking paths and country roads. You can do similar on the plane and hills of nearby winegrowing region of Peljeska Zupa.