Right bank, immediately above Henley Bridge.
The Angel on the Bridge website.

Their loos are through the door facing the river, furthest from the bridge.
Where to park?

Henley Car parks

Note that several pictures of the Angel are in the Henley Bridge section
The Angel on the bridge is said to be 14th century.
Indeed the original Angel may well have been more 'on the bridge' than it is now. The old wooden bridge on stone foundations was to the south of the current bridge, (that is on 'the Angel' side) and one of its foundations has been found in the Angel cellar.

1829: A Tour on the banks of the Thames -

The town, as it now stands, comprises several fine streets, wide, well paved and lighted, and possessing that cleanliness which gives to every thing a double charm. There is also in its neighbourhood, numerous beautiful walks and drives, making Henley altogether a deserved favourite with the numerous class of persons who find occasion to visit it, whether for business or pleasure.
It also possesses several good inns, and among others, that of the Angel, situated at the foot of the bridge on the town side. The civility experienced by the author from its host and hostess deserves this mention of their house, and their reasonable charges and good accommodation ensure it. Here may be had pleasure boats, as also a variety of punts for fishing parties, of which numbers are to be seen every evening on the river, adding, by their presence and picturesque appearance, an additional charm to the scenery around.

1856: George Leslie, "Our River", writing in 1881 -

It must have been about eight years after my adventures at Hungerford Bridge, that I paid my first visit to Henley, where I spent a few weeks with my brother-in-law.
[ George was born in 1835 and was 13 he says at his "adventures at Hungerford Bridge", so he was about 21 in about 1856 on this first visit to Henley. ]
We stayed at Mrs. Johnson's hotel, "The Angel", and had as a sitting-room the upper one with the quaint bow windows, from which a view was obtained of the bridge and the race-course. I never saw Henley Bridge without some one looking over it at the river below. It is a most fascinating bridge to look over. All bridges are delightful to look over, but Henley is the best in this respect I ever knew. There are landing places for boats on either side, and always just enough going on to gently interest one. The stone balustrade is exactly the right height to lean on, and there is a ledge below, which seems made on purpose to put one foot on; indeed it has been well used in this way, as between the base of each little pillar of the balustrade the stone is worn into round hollows. There is at one corner the thick foliage of a plane tree, under which one can pause during a shower, and the open balustrade lets the cool air play gently on your legs in hot weather. I never walk over Henley Bridge without stopping, and indeed, believe no one else ever does.

1870: Blackwood's Edinburgh Magazine -

That night we slept at Henley under the guardian wings of the Angel, who gave us a bow-windowed parlour on the river, and treated us tenderly and charged us still less than the Lamb.
The Lamb and the Angel ! Gentleness breathes in their very names. O Highland innkeepers, would you but learn their touching lesson! Whereas we think of you with dread and horror, or at the best with awe and trembling, those soft names swell mellifluous in our memory.
The Angel at Henley is not unknown to fame. It commands the winning-post of the Henley regatta, prettiest and gayest of river festivals.
Opposite, with one willow drooping into the water, is the little bit of ground fondly known to Eton as "The Lawn," whence the school champions issue forth to win their yearly race.
To see the river now, so quiet, so lonely, and silent, in the full moonlight of the summer night, or breezy freshness of the morning, is strange after our last glimpse of it on the great Henley aquatic festival.

1873: Advertisement -

1873 Advertisement Angel, Henley
1873 Advertisement

1881: The Angel on the Bridge, George Leslie, "Our River" -

Angel on the Bridge, Henley, George Leslie, 1881
Henley, The Angel on the Bridge, George Leslie, 1881

1899: Boating down to the Angel on the Bridge, movie -

1899 movie of The Angel on the Bridge, close up of the riverside facade

1950: The Angel Hotel - Eric de mare

The Angel on the Bridge, 2015, Doug Myers