Robinswood (Frensham Trout Fishery) near Churt (between Farnham and Hindhead) offers a range of sporting tickets - all day, half day or evening. Five clear spring-fed pools between a quarter of an acre and one and a half acres set in a very pretty wooded valley. Can get busy on weekends, but offers excellent sport. Highlights are the early spring buzzer hatches, consistant mayfly, late season daddies and sedge.
Kingfisher Lakes at Hammer (just off the A3 south of Hindhead) used to have three small trout pools at the top of a chain of seven; I haven't been there for a while and there were rumours that the trout pools were going to be filled in to make a nine-hole golf course, but I don't think that has happened yet - if it will at all. I have enjoyed some excellent sport there and caught my biggest brown - 5lb+ - on a size 20 dry midge from the middle pool. It was also incredibly cheap.
Meon Springs between Petersfield and Winchester has a catch and release section which is really an impounded stretch of a headwater of the Meon. It can get partially choked with silkweed during the warmer months and the banks are very exposed, making casting tricky if there is any sort of wind. Very picturesque nevertheless, set in a quiet chalk downland valley. There are two main lakes as well which are strictly put and take; there are some big fish to be had to stalking tactics, and unused fish credits can be used on subsequent visits.
Hope this helps. Like you, I find I catch more trout than I can eat; my local pub benefits accordingly!