Burley, New Forest
Suppose it depends on how far you're happy to travel from the village. Obviously you're close to Southampton, Salisbury and Bournemouth. Can recommend WestBeach in Bournemouth
On the immediate New Forest patch - Master Builders House at Bucklers Hard (decent pub food)
No experience of these but, in the Forest area, Harden's also has the Montagu Arms Hotel @ Beaulieu, The Pig ~ Brockenhurst, Egans @ Lymington and Hartnett Holder @ Lyndhurst.