Oruro Carnival if you are in the country in February or March--it's absolutely amazing and only a 4-hour bus trip from Cochabama. Beware of hiked bus ticket and hostel prices for this weekend!
Everyone's got to climb the Cristo, especially as it's less than a metre taller than the one in Rio! I went by cable car today, which does provide wonderful views!
Quick Tips:
Always get small notes of the local currency; as there is a shortage of change in the country, banks have to, by law, "fracionada" large notes, but don't try too early in the morning!
Best Way To Get Around:
Taxis are incredibly cheap, but truffis are much more fun and will drop you off anywhere along their route. They're also very cheap and cost 2 bs to get to Quillacollo 45 minutes away (about 20p).