The Master Builders House Hotel at Bucklers Hard on the Beaulieu river is lovely. Pub bit with food and a smart restaurant. The same proprietors also have the well regarded East End Arms between Beaulieu and Lymington, and The George Hotel in Yarmouth which is a short ferry trip from Lymington. If you do go to Yarmouth you might want to walk 2 miles up the banks of the River Yar to The Red Lion in Freshwater which is excellent. Just outside Lymington on the New Milton side is The Chequers which is well worth a visit.
Winchester - Chesil Rectory (Currently under new ownership, Black Rat (excellent quality food, hearty eating in low key restaurant, Gandhis (Best curry in town)
Brockenhurst - Le Poussin at Whitley Ridge (fantastic set lunch in Michelin starred hotel restaurant http://www.whitleyridge.com/whatsnew....)
East Chisenbury (Salisbury Direction) - Red Lion Freehouse (this was my secret place until Rayner reviewed in OBbserver last week. Best food I have eaten in a long time, amazing wine list from fantastic wine merchant near Winchester, Stone Vine and Sun)
Lyme Bay - Hix Fish and Oyster (good food, but amazing setting over the bay
Hope this helps a bit