If you stay in the centre of the city you'll have no problem finding a hotel that's close to the metro. Like in any big city, some neighbourhoods are better than others. I would highly recommend St. Germain or the Marais, both of which are really charming areas in Paris -- central, easy to reach the big attractions, plus near restaurants and cafes. And they are safe for females on their own.
Having biked in the US all my life, where biking makes you a "rebel" making a political statement, it felt very strange to suddenly be in Copenhagen in a context in which cycling made you a normal person. For myself, I think I have come to realize that I am willing to make that identity change for the trade-off of living in a bike friendly society.
Barcelona … I do recommend staying in the Gothic because it’s really the heart of what’s happening in the city. Just be aware, and stay clear of the following places -- La Rambla, (also known as La Rob-la), the Metro (one of the places I’ve seen the most robberies, averaging one sighting a week), and Calle Ferran (filled with drunk tourists).
