Not sure you'll be able to get that close to the dome. Taxi rank is closest and if you tell security on a concert night you are dropping at tube station they sometimes let you past.Dropped pin
near 5 Millennium Way
London SE10 0PH
http://goo.gl/maps/Y5Dh0
Sundays within square mile will be deserted. Lookup Threadneedle or blackfriars. not so good with the bars but head to Liverpool street or bishopsgate for that. Parking a bit trickier. Head to hoxton for a drink. Or further into town here...The Old Red Lion
http://goo.gl/maps/Ak0ji and kimchee for grub.
Kimchee
http://goo.gl/maps/tvxxD
tunnel under black friars at baynard street, watch out for speed camera when you return to main flow in daylight. Turn left up Lambeth hill just before the speed camera to do it all again via Queen Victoria street and puddle dock. Blink and you'll miss it though and be heading south.
Castle Baynard Street / Puddle Dock
http://goo.gl/maps/GZva0
Use street view to see what I mean.