I drove to West Hampstead from Brighton for about 3 months. It could be a real beast of a journey and the only suitable route is really A23/M23/M25/J16/A40. I was going to say leave at the crack of dawn, but you are going in the middle of the day.
I ended up taking the train in the end to avoid a trip to The Priory.
I do need to drive as I'll be picking someone up on the way to a festival. I suupose I could get them to get the train to somewhere easier if it's as beastly as it sounds.
Soul Finger - yeah, nearish there. Kinda between West Hampstead tube and Kilburn Park as the crow flies.
Never drive into London up the A23, as soon as you hit croydon it is shit. As a rule I use the A3 for west London and the A2 for east london. Kilburns a bit further up though so I'd consider going M4 and then get on the north circular.
Edit * just read BoFs post, A40 is another option, a bit further but cuts out the shit part of the NS between chiswick roundabout and hanger lane.
I would go M25 - A3 - A306 (Barnes, Hammersmith Bridge) - round Shepherd's Bush Green - up Holland Park Ave - left onto Ladbroke Grove, then all the way along and right into Kilburn Lane. Although you will get congestion-charged if you're going in the week.