There are bus and metro services, the city centre is huge and you can find different atmospheres. The views from the bridges and cathedral tower are amazing. You can get local food for a reasonable price. I found an excellent free tour very interesting (in English), you can walk for hours and hours, there are parks at both sides of the river. The "crane buildings" area is nice. Plenty of shopping areas for buying anything and museums to go. You'll find interesting architecture.
Insider Tip:Go to both sides of the river. For partying go to AlterMarkt and along Hohenzollernring. Cheap local food, beer and restaurants by the other side of the river, opposite the old city centre, between Hohenzollernbrücke and Deutzer Brücke, good sights from there as well.