Well you have to visit Sandy Balls campsite, don't you, just for the name...
I'll also reccommend the Ornamental Drive from Brockenhurst north-westwards.
A nice circular ride that includes this is something like this (you'll need an OS map):
Brockenhurst - Rhinefield Ornamental Drive to cross A35 at SU267 063 - Bolderwood Ornamental Drive to cross under A31 at SU236 097 - turn R at T junction to cross Ocknell Plain (site of a WWII airfield; the road used to be a runway) - left at T jn at SU 247 131 to visit Fritham and the highly recommended Royal Oak for lunch. Then retrace your steps to the T junction but carry on southwards to cross the A31 again at SU257 117 (you'll have to run across and lift bikes over the central reservation - there's no "legal" crossing here). Continue to Lyndhurst, then onwards on the B3056 to Beaulieu, where you can visit the Motor Museum, or just eat cake.
Tearing yourself away from the cake supply, you now have the choice of returning to Brockenhurst directly via the B3055, or taking a more roundabout but scenic route to Bucklers Hard (historic boatyard, maritime museum, mariner's cottages etc.), then turn west to Sowley Pond, Norleywood (whose Youth Hostel is much missed and fondly remembered), Lymington, Mount Pleasant, Durns Town and then Brockenhurst.
Mrs Uncle Phil and I managed this in a short winter day, so I'm sure you can manage it in a long summer one. We planned the long version, but did the short one (we stayed too long in the Royal Oak - but it was COLD outside back in December).
The New Forest is pretty flat and there's a blanket 40 mph speed limit on the smaller roads to limit the damage to the ponies who like to stand in the middle of them. Between them, these things make the cycling very pleasant.
You could consider a jaunt across to the Isle of Wight on the ferry from Lymington. If you do, stick to the southern half of the island.
Enjoy.
