Tokyo dialect is almost the same as standard Japanese.
I rejected Koichi's request that I speak in Tokyo dialect.
"I need to get some free Tokyo dialect lessons." "Ask Koichi. He’ll do anything."
You know that 東京 is Tokyo, and you know that 弁 is dialect, so you have yourself Tokyo dialect.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well. It will help to know how to read 東京 already, which you should.