A few good ones by the river behind the apollo. Next to the bridge. High st pubs are shit unfortunately. Distillers on Fulham palace road is also good, but can get rammed
I've not found anywhere really great round there but the Distillers is decent and near the tube and The Blue Anchor and The Dove on the river are both nice but a little further away.
Where is good in Hammersmith? Within five minutes or so of the tube would be great, but further afield is ok if there is somewhere worthwhile.