Do business.
People say you need to have a drink to do business, but I don't think it works for me as a woman. Honestly, the business dynamics are a little different among the sexes.
Networking/meeting activities that work for you:
2 guys - go grab a beer
2 women - go grab lunch
Man + woman - go grab coffee
I personally never network/take business meetings with a man while getting a drink. Once a man gets alcohol in him, generally speaking, he switches his focus from business to boobs. Coffee is short and gets the job done.
Women talk a lot, which is why lunch works for them.
Men bond over beers.
I am a woman. I do not need to drink to do business.