Are you sure "accost" is the word you mean? "Accost" means to approach someone to annoy or harass them (dictionary:To approach and speak to boldly or aggressively, as with a demand or request) so it's not really the right word. I think what you might be wanting is "to go up to someone" or "to approach someone", but it still doesn't convey the right sense.

From your context I would rather say you mean 'stalk someone' ??

I think this question for females more than for males.

I have had conversations with many strangers in countries I have visited. However, I have NEVER given them my phone number or where I am staying. Be very careful.