Well, I would hang out with a lot of the characters, at different times and for different reasons:
I would love to talk about books and demons with Giles and Wesley, about music and life with Oz and about science with Fred.
Tara and Willow could give me a magic for dummies beginner's class.
I'd be great to shop with Buffy or Cordy (not at the same time 'cause they aren't very fond of one another) and also Anya.
I would love to do something artsy with Angel, but since I have a huge crush on him, I'd probably be too anxious or intimidated. I could, however, just stare at him any time of the day and/or listen to him talk about his life and important historical moments he experienced first hand.
I would also like to do something with Lilah - preferably of the legal and non-life-threatening variety.
Finally, I would hang out with Lorne. Whenever and however he wanted. I would even sing karaoke for him, though I'm pretty sure he wouldn't want me to.
There are a lot of cool Buffyverse characters to choose from... I would even hang out with Andrew - who's not cool - under certain circumstances (for example, to make fun of him).