coolio, 10 aint too early so i'll see you guys there.
And as DT says, its congestion charge free at weekends but parking anywhere in the zone is gonna be tough unless you know london like the back of your hand and are willing to spend a fair amount of time zig zaging about finding spaces.
you may be better off to do the touristy thing and park up close to a tube or bus station and buy a travel card. If you do make sure you go to oxford street and get your moneys worth from it by getting on a bus for only one stop and then getting off and getting on the next bus for another stop and repeat until bored.
At this time of year the buses on Oxford street are so many its like a train of buses and you two are just silly enough to enjoy doing it too.
Me and my friends used to do it when we were kids and all the buses were routemasters, we just didnt bother with the travel card bit cos you'd jump on, the conductor would ask where you were going to and you simply told him a destination that you knew full well was in the opposite direction, hey presto he'd say "get off at the next stop then, you wanna be going the other way". Used to get about most places in london that way if truth be told and god help me, i remember that the child fare in those days was only 2p!