Although I live only just over a mile from the city centre, this is something of a 'leafy suburb' and I have a decent garden. Consequently, there is a fair bit of wildlife to be enjoyed - currently a pair of rival grey squirrels are providing much entertainment, and we have begun feeding them.
Another pair - also presumably rivals - are the nightingales whose unsurpassed singing (equally as-good-as but different-from the many virtuoso blackbirds) is easiest to hear after dusk and before dawn - each nightingle showing his ability, then listening to the other, in cycles lasting several seconds.
Woodpeckers (Great Spotted) are another species that exchange messages - in their case drumming as loudly and long as can be managed, until the opposition gives-up from feebleness.
There are flocks of jackdaws who come to feed - these being seldom seen until the past decade. Magpies have always been common and dominant; wood pigeons are beautiful, abundant, loud, and make an appalling mess on the grass and everywhere else.
Among mammals there are foxes - emitting a wide repertoire of blood curdling sounds, and (unless the holes are blocked) digging holes in the lawn and bringing their cubs to play.
One thing I haven't seen for a long time is a hedgehog. There used to be plenty, but as the above species have waxed, the hedgehogs have apparently waned - which I regret.
There are mice and frogs in the longer grass around the edges - although seldom encountered.
Once, a single snipe/ woodcock came and fed on the lawn when it was covered in snow - leaving hundreds of circular holes where its beak had been probing...
There are also large amphibious rats in the vicinity - although I'm pleased to say I've not yet seen one in the garden...