>>798500go to the east side of Bath, there are lots of walks around there, like the walk all the way from Batheaston out along to Box up to the quarry which has a nice view back down along the Box valley, or you can follow the bridleway from Batheaston up onto the top of the hill where there's a wooded bridle path and a big green space. Or take the path from Batheaston up to Bathford and if you can find it there's a path leading from the estate up into the Area of Special Scientific Interest (protected woodland) and that path takes you up to a "folly" and from there out onto the hill with views out over Wiltshire all the way to the Salisbury plain. There are also footpaths along the river from Bath to Batheaston, and a nice walk through Larkhall and up across Bailbrook, where there are horses, a lot of trees and bird life with excellent views, I recommend that one. Also from Bailbrook there are footpaths leading up the valley.
Also there's obvious ones like following the canal from Widcombe in Bath all the way up to Batheaston, or start at Batheaston and walk along the canal where it turns to the south - along that route there's Claverton Weir where there's a swimming place, although it's mildly dangerous and people have died there. Then if you continue along that canal path you end up on the Collier's Way
http://www.colliersway.co.uk/Areas_covered.php which you can take all the way to Frome if you're up to the walk - however some of the Collier's Way is on a small road with no pavement or even grass verge and poor visibility so it's risky.
Less obvious is heading up from Widcombe and making your way into the maze of lanes and backroads which lead up to Prior Park, and then there's also some kind of large open plain of with a lot of trees up above Bathwick (the other side of it from the river).
Alternatively in the other direction there's taking the Bath/Bristol cycle path on the old railway, that might be risky in terms of anti-social people though.