Neighborhoods west of downtown are mainly residential. Some are middle-class and some are poor. Unless you're a local, it's hard to know which areas are safe and which are not, so you should avoid wandering around. One exception is pleasant Quinta da Boa Vista, which is fine to wander. You can easily get here by metro, but avoid coming after dark.
Few visitors will make their base in the area west of downtown, but one compelling reason to visit is the mighty Maracana soccer stadium, which is open for tours on non–match days. If you want to catch a game it is easiest to go as part of a group trip. Nearby, the city zoo, national museum, and scenic gardens at Quinta da Boa Vista are worth a visit if you have the time.