not public but restaurants and bars have facilities

You can get the Piccadilly line from Piccadilly Circus to Russell Square station. It's four stops and should take you roughly 15mins.

Le Meridien Piccadilly is a beautiful hotel very close to Piccadilly Circus! There is also the Radisson Blu Edwardian Hampshire hotel or Victory House hotel, both located in the heart of Leicester Square only seconds away from Piccadilly Circus

Περπατώντας θέλεις περίπου ένα τέταρτο. Με το μετρό θέλεις περίπου 7 λεπτά ή πάρε δυόροφο λεωφορείο, κανένα δεκάλεπτο λίγο-πολύ ανάλογα την κίνηση.

If you think Pizza is one of the best places in central London I suggest you broaden your horizons. I would head for Chinatown ....very close

There are no lifts at Piccadilly Circus station, just escalators and about 40 steps up in total from train platform to ticket hall and street level. If you are travelling from Heathrow, take the Piccadilly line to Green Park, where there is an escalator from the train platform to the ticket hall and a lift from the ticket hall to street level.

Non lo so mi spiace