Book a flight and a hostel and you'll have a great time and will meet loads of people. It doesn't matter if you arrive on your own as you will meet loads of people and spend the time with them.
I don't know about cheap but San Francisco and Vancouver are both entertaining and lively cities that might be worth investigating to see if they've got any suitable offers. I would have thought that 4 days would be a bit on the short side as a trip considering how long it takes to get out there but if that's the holiday time you've got available then that can't be helped.