Not only can you see deer in Richmond, but it's also a great place to spot the occasional heron, as in the picture below. Now, I have mixed views on feeding wildlife (pros: you get to see them closer, they don't get hungry. cons: they become used to human activity which may have further detrimental effects, but nonetheless you can always watch other people feed the geese, ducks, pigeons (I'm *not* a fan of pigeons) though.
Richmond Riverside is a great place to go for a stroll and there are a number of eateries/cafes in the area. Although there didn't seem to be much on the other side other than shops, Richmond Bridge is still quite a novelty to walk on. There are also boat trips (and boat hire too I think!) if you feel like something a little different.
In the picture below you can also see an island - which is the land with the willows on it that the boats are next to. There are quite a few islands dotted all along the Thames until a fair bit upstream (to name a few: Isleworth Ait, Chiswick Eyot, Eel Pie Island, Monkey Island etc). Quite a few of these and the banks have willows on them. These were grown for the basket trade for the London markets in the old days.
Get there: Richmond station, various buses from west/south-west London.