I used to dispatch ride in central london, best bikes all had similar characteristics.
Light, narrow, torque+++, upright seating, straight bars + cheap,-> SuperMotad.
typically a twin, V or parallel, KLR, Vstrom 650, KTM, DR-650.
Some small I-4's no bigger than a 600 (not a GSX or CBR, look at a Bandit).
Regear it lower, acceleration is your friend not top speed.
Why cheap, it's going to get dinged and the high risk of theft in the city.
Forget the plastic, you will only have to repair it.
If you are going to put cases on it get metal ones.
Also a monster chain and lock it to something solid.
Hand protectors and engine bars highly recommended.
Also buy a pair of big arsed MX boots and heavy gloves.
It's a rough environment for a bike and rider.