Inviting Someone

Do you want to / wanna (very informal)
Would you like to
Will you . . . (with me)
How about V+ing
How would you like to
I was wondering if you would (like to)
I would like to invite you to (more formal)

Conversation practice

When inviting someone to do something with you, it is polite to "break the ice" before extending the invitation.
For example,
Will you go dancing with me on Friday? (too abrupt by itself)
(Give the other person time to "prepare" for your invitation.)

A: Do you have time on Friday?
B: Yes, I do. Why do you ask?
A: There's a dance at the Grand Ballroom.

A: Would you like to go with me?
B: Sure! I'd love to.

Bob : Alice, what are you doing Sunday afternoon?
Alice : Not much, what did you have in mind?
Bob : The Fourth Avenue Street Fair is going on downtown. Would you like to go?
Alice : Sure, sounds like fun. What is it anyway?
Bob : Just a bunch of vendors selling food, clothes, and what not, kind of like a carnival.
There are also street musicians and performers.
It's interesting to just walk around looking at the people and the sights.
Alice : What time and where do we meet?
Bob : The fair opens at 9:00, but I'm busy in the morning. How about 1:00?
Alice : OK, should I meet you somewhere there?
Bob : Why don't I pick you up at your house?
Alice : Sounds good, see you then.