If you don't mind a drive from the New Forest north to the Salisbury area, Avon Springs is a very good fishery - 2 lakes and a nice stretch of the Upper Avon. The fish are good quality as they are not pushed too hard in the stews, which are running water, so the fish aren't flabby "pellet pigs" and have a reputation for being good eating.
http://www.fishingfly.co.uk/
I agree with Howard's comments about Holbury - a nice stalking water again with good quality fish. Stalking browns in the quite overgrown little River Dun there - they stock it every year but the fish quickly wise up - is specially good fun and quite challenging.
If it was me, I would give Avington a miss, mainly because it's now quite an expensive day out for what you get. Take that money and add just a few pounds to it and you can have a day on a reasonable chalkstream beat like those Richard Slocock offers on the Dorset rivers.