I've lived in/near Keene for 10 years now and wish I could help but I am not much of an outdoors person. (Love living here though.
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I have seen people fishing in little lakes/ponds around here (e.g. in Swanzey). The Lakes Region isn't too far away for weekend trips, I imagine the fishing can be great there!
Sorry I can't help much but this will bump it up and hopefully others will chime in!