1) Stay in hostels, but do your homework. "hostelz.com" is a great place for good, honest reviews. (Some sites only accept positive reviews, which kind of defeats the purpose if you ask me). Most hostels have very good accommodations, have attentive owners that can give you more personal attention than a hotel, and you get to meet cool people if you're feeling social! I have stayed in quite a few hostels and always manage to meet somebody or a group of somebodies that take pity on the lone female traveller and treat me to dinner, drinks, etc.
2) Always travel the city on foot or use public transportation. I never felt truly connected to a place when I travelled as a young lass because the adult with which I travelled always had/rented a car. When you explore the city on foot or use the buses/trams/subway, you get a much better feel for the city, the people, and the energy of it all. It's also a lot cheaper than renting a car and in many big cities, parking costs you a lot of money!
3) Have your biggest meals at breakfast and lunch because those are always the cheapest meals at a restaurant. Most restaurants get the majority of their clientele for dinner, which is why sometimes you can buy the same thing for dinner that you had for lunch and it costs significantly more. Fill up on a good first two meals of the day and then have an appetizer or very light supper. Another good tip about food is if you are staying at a hostel you can buy your own food to prepare and store it in the kitchen. I would prepare two meals a day and go out for one, except for one of my extended stays where I only ate out two or three times a week.