The Royal Oak at Fritham is always a good place to visit, nice bit of the forest and cracking Ale.
Was right outside there today, but with a gaggle of 15 year-olds in tow, I had to give it a miss!
Bushwhacker is right, Bolderwood is worth a visit to see the fallow deer which come there to be fed (though the car park does get a bit "grockly" at weekends). It is quite near Lyndhurst too, which has an excellent visitor centre and museum. If you do go to Bolderwood, stop off on the narrow road that leads north to it from the A35 and have a bimble round Marks Ash Woods. Marks Ash is one of my favourite bits of ancient woodland and from Mid-April onwards is full of breeding birds such as Redstart, Wood Warbler and Lesser Spotted Woodpecker.
Another great area to explore is the heathland and woods around Beaulieu Road Station, which is about 3 miles east of Lyndhurst (park in Shatterford car park). Again, another good place for birds and dragonflies (in season) and there is good mixture of habitats.
Let me know if you need any directions and/or grid refs. Also if you think of anything specific you hope to see, give me a shout and I should be able to point you in the right direction.