Teddington Lock is the end of the tidal Thames, which you can see without a lecture. Below the lock the river still rises and falls. Above it, the water sits in a managed pound toward Kingston. That change is the reason a walk from here feels different within a mile in either direction.
Downstream toward Ham and Richmond
Cross at the lock and take the towpath toward Richmond. The first stretch is wide and open, with Eel Pie Island off Twickenham and then the long view into Richmond. It is an easy hour if you do not stop, and a better two hours if you do. The path is busiest on a sunny Sunday afternoon. A weekday morning is the same walk with room to stand still. Richmond is the natural turnaround: a coffee, a look at the bridge, and the path back. You do not need to go into the town unless you want to.
Upstream toward Kingston
The other way is quieter and more ordinary, which is its advantage. The river above the lock is a working pleasure-boat channel, and the path into Kingston is a local walk rather than a postcard. It suits a short outing when the downstream path is crowded, and it suits anyone who wants to end at a station. Kingston has trains. So does Teddington. You can walk one way and ride back.
Practical notes
The lock footbridge is the hinge of both walks. Check you are on the path you meant after you cross. Wear shoes you can scuff. After rain the downstream towpath holds puddles and the occasional bike that is going faster than the sign suggests. Dogs are everywhere on fine days. None of that spoils it. The river is the point, and it is doing something different on each side of the weir.
If you only have an hour, walk downstream as far as the view opens up, then come back through the lock. You will have seen the tidal river and the still one, which is the whole idea of starting here.