I have some surface rust around the strut mounts on my car (yes, I've checked, it's surface, no holes). This is beyond my ability to repair. Is this something I should be taking to a mechanic or body shop?
If it's only surface rust, it's really easy to repair yourself. All you have to do is use a wire brush to clean the spot, then put a rust inhibitor like POR-15. The rust inhibitor will keep it from rusting again. When I say this is easy, I mean really easy. Really, a body shop should tell you the same thing (unless they are wanting to make some money).
Be careful when using POR-15 as it will stick to whatever it comes in contact with. Use a paintbrush you don't want to use again. Use up the entire can, as when you put the top back onto it, anything in the lid crevice will cause the lid to permanently weld to the can. Use nitrile gloves and safety glasses.
I'd start making some calls to body and mechanic shops around you and find out who would be comfortable doing that. It's hard to absolutely say one or the other because this feels like an area that both could conceivably take on, and really depends on the shop's setup. A lot of places will also outsource anything they can't or won't do, so you may just be able to bring it to whatever's nearby.
I would also call your local dealership and see if your car has any recalls regarding this. It may qualify you for free repairs or even a buyback if the damage is deemed to be bad enough. It'll also be nice to have the work on record with the dealership if it gets worse or shows up again in the future.