Funicular side of the famous Chain Bridge, turn right up the side street and visit the quirky bar/cafe on your left about 30 yards up the street. Full of old curios/memorabilia. Old Toy shop a bit further up the same street same side.
Walk/Tram to Green Bridge. Near there is a great indoor/outdoor market place - plenty of bars/cafes.
Basilica and up to the Castle a must.
Dreha!