hello there,
speaking as someone from winchester there are several good birdwatching sites within the city and surrounding countryside. here's some top tips (grid references of entrances, car parks, viewpoints etc)
winnall moors - reedbeds, river, woodland, scrub and water meadows, common riverside birds including cetti's warbler, little grebe, reed bunting etc, water vole likely, chance of kingfisher (SU 486 296)
winchester sewage farm - okay so not the best smelling location but large numbers of gulls + lapwings, plus other waders likely, hobby possible and chats often in the vicinity at this time of year + other migrants. viewable from the layby on Morestead Road (SU 490 279) rarities have included black-winged stilt, cattle egret, pectoral sandpiper, grey phalarope etc
winchester water meadows - cetti's warbler, water rail, reed bunting, water vole, grey wagtail, kingfisher etc all possible along the river and in the water meadows. rarities have included little bittern, little auk, yellow-browed warbler, cattle egret etc. parking at St. Catherines Hill (SU 483 280) then following the public footpaths
if you're willing to go out of the city a bit there is cheesefoot head and longwood warren (cSU5227) which has breeding Corn Bunting, Hobby etc, and Quail have been calling this year, might be Red Kite there as well