Definitely use metro within the city proper- I am a single female who has lived in the city for almost 5 years- I always take metro.

It is really safe, clean and tourist friendly. I would imagine any tourist attractions or dining, nightlife you are interested in would be in a safe area. If in doubt about something, ask us here. I probably tend to the paranoid about going places alone as a female at night perspective, but am fairly good at channeling my calmer friends to give their take on places.