For longer term storage Broccoli freezes well.

Storage Req: Freezer
Storage Temp: 32°F
Storage Length: days

Broccoli is best eaten as soon as possible, as it is quite perishable. It may keep up to a week or so in a plastic bag in the fridge. 

Storage Req: Refrigerator
Storage Temp: 35-40°F
Storage Length: 3-7 days