There's a really nice family run Italian restaurant near the cinema on Ken High. The food isn't too expensive, and the food is very hearty and authentic. It's quite simple inside and a lot of the people are local regulars and sometimes you see an old celebrity. The staff are extremely friendly and acommodating.
http://www.ilportico.co.uk/index.php
Near South ken there's a very authentic french fish restaurant. It's moderately priced and all the fish lovers with me really liked it. Give it a miss if you're not into fish... It's called Le Suqet, off Fulham Road.
There are many other slightly more expensive places from gaucho grills to pan-asian etc.
-aucho is definately worth a try for a meat fan.
-Le colombier has great modernish french food
-Daphne's is a classic italian from the 60's although its been bought by a group now... Still, it's a place to visit, the food is good and you might see someone famous from back in the day
These are just the ones i've tried, and all are the kind of place I'd recommend to friends, but Il Portico really stands out to me. Over the years I've been with my parents and visiting family, with friends, dates etc.