I live in Broadmayne just over the ridgeway north from Weymouth. Puddletown is good for an hour or two’s blast. You will have to do a lot of climbing though, nearly all the trails are either up or down, not much flat. Lots of singletracks have been created just off of the main forest trails, just pick one and go for it. Its not a huge area, about 2.5km by 2.5km and bounded by quiet roads on three sides (south, east and west) and the fenced off dual carriageway (Puddletown bypass) on the north side, so you cannot get lost (for long). There are usually plenty of locals there so always some to ask about trails or the way back to the car. Best parking are the bays on Rhododendron Mile on the eastern side, 90% of the forest is then to the west of you. I would also suggest the South Dorset Ridgeway to Hardy’s Monument. Use the Weymouth/Dorchester cycle track to leave Weymouth and at the top of the ridgeway go east on the bridleway that runs right along the ridge to Hardy’s and Abbotsbury, the views are stunning to the south and north. Either come back the same way or descend into Abbotsbury, use the old railway line track to Portesham then take the quiet lanes thru Coryates and Friar Waddon to get back to Weymouth. Don’t use the B3157 its a racetrack! There are some nice bridleways and quiet lanes to the south of the B3157, thru Rodden, Langton Herring and Chickerell, best to a get a map if you want to go that way though. Portland is also great fun, but you need to know your way around as its all designated as “footpath”, however all the locals ride it as the vast majority of the trails can accommodate walkers and cyclists, some hairy cliff top bits on the western side. Have fun.