Shadowing / Work Experience: best place to contact firms?

It can be difficult with smaller, local law firms as they don't have the same "back office" resources, such as a big HR team, in place at the larger firms. You're right, therefore, to consider this properly.
I would call their main contact number. That's likely a receptionist who will be able to direct your call, take a message or give you the best email address to contact. Make some notes beforehand of what you're calling about and what you're asking for e.g. "Good Morning, this is John Frogger - I'm a Year 12 student at Lily Pond Grammar. I'm looking to secure some work experience this summer and I would be very interested in some form of shadowing opportunity with Bstard & Scrooge. I don't know whether the firm can accomodate that, so I thought I would call. Could you tell me who I should contact, please?"
At worst, they'll take a message and promise to come back to you. At best, they'll give you an actual number or email address to contact. At least then you have a "real" person to chase up, rather than a general email enquiries email which will disappear forever into the void of Bstard & Scrooge's email server....
You'll need to be persistent. Small firms are often overworked with little time to consider these requests. If you do get a chance to speak to someone about the possibility of some experience, then be incredibly polite, offer to do anything and everything and to do so on an unpaid basis.
Best of luck!