This is certainly an important decision that deserves some forethought.  The primary decision is indoors or outdoors.

Indoors

The advantages of an indoor bin are:

• It will stay warm (& therefore more active) in the winter.
• It’s convenient.
• You won’t have to rodent-proof the bin (assuming your house is rodent proof!).

Disadvantages:

The indoor bin needs to have a drain spout, whereas outdoors you can just drill holes in the bottom & let the bin drain onto the soil.

You might have to win a debate with your spouse/housemates that it will not smell or attract insects (which is absolutely true if maintained properly).

Outdoors

If an indoor bin is out of the question, it should be as well protected from the elements as possible - at least out of the rain and direct sun.  If your winters get very cold, you may want to lay soil warming cables at the bottom of the bin (see Winterizing Your Outdoor Bin).  In that case, you’ll need to put the bin near a safe electrical outlet.

Consider there will inevitably be some excess water dripping from the bottom of the bin.

Be aware that it will probably attract the attention of rodents, but not to worry, there are ways to keep them out.    See Keeping Out Rodents