You can make a nice loop fairly easily – it won’t be at all technical though. I normally ride it on a gravel bike.
Head north through New Milton and have a mess about in the Brownshill / Wilverly / Helmsley Enclosures. When you are done there, head east on the disused railway line that brings you out at Setley Common. Cross the main road. There is a fun bridle way (might be a footpath, can’t recall…) that starts just south of Brockenhurst Park and heads south. When you are back on the roads, cross the Lymington River and remain east of it until the bridge at Walhampton. Then ride south through Lymington and keep the water on your left – you should pick up the sea wall by the Yacht Haven (good pint / coffee at The Haven…) The Sea Wall will take you round the salt marshes to Keyhaven – then follow the coast back home.