student search for a accomodations

My name is Anastasija. I am from a small Baltic country Lithuania, but during next 4 or maybe even more months I'm going to study in Budapest. I'm a 20 years old easy-going, open-minded and responsible girl, who is looking for a cosy room in Budapest for affordable price. Also, I'd be really grateful if some locals or just youngsters of my age who already know Budapest could show me some places of interest and could inform about different nuances as public transport, mentality of the people and other things. I'm fluent in Russian, Lithuanian and English.