tyrion

I don't have a socket that will fit in this pedal to get to that nut. Any recommendations for a socket set that will have a socket that will fit in that hole? Not much gap between the nut and the surrounding structure.

(by "not too expensive" I mean Nashbar quality, not Park Tool.)

Iride01 

I'm not familiar with those pedals. But be sure the entire spindle doesn't just unscrew from the other side, the nut you see in the photo included. For most of the Shimano pedals I use, that requires a special Shimano tool to unscrew. Once the spindle is out that nut on the end of the spindle is easy to get to.

SurferRosa

I use the same $8 Sears socket set that my dad gave me when I was 10 years old, which is kind of cool. I think it's the only physical thing I have from him (RIP).

I've only added one socket, which is a thin wall 15mm for crank bolts. I would advise the same: a very cheap socket set (Harbour Freight?) and then simply add to it with the few special sockets that you need. ie: Take the pedal to a hardware store and buy an individual one.

tyrion

Those are Rock Bros pedals (cheap but big). I just found a video about taking them apart - it looks like there is a sleeve in there that is causing the socket clearance issue and that sleeve is removable.

Mad Honk 

I would recommend going to a pawn shop and look in the tool bins. All three of the ones near me have them and they have sockets from the cheapest to some of the most expensive. A cheap socket will usually cost $1 or less. A Snap On socket goes for about eight dollars. I have a number of tools in my tool box that came out of pawn shops just because of the very discounted prices I paid for them. And they still have the tool truck warranty as well. Smiles, MH
Correction: I stopped by one of our pawn shops today and inexpensive sockets are 10 for $1.

HillRider

Another good source of tools from dismal to excellent quality is the local flea market. There will be vendors with big piles of of Asian sourced junk and other sellers clearing out their own workshops or conducting house/estate sales of excellent name brand tools at very good prices. A couple of years ago I bought a Stanley "Bailey No. 4" wood plane is somewhat rough shape for $3 at the local weekly flea market. A few minutes with a wire wheel, oil can and sharpening stone and I had a fully serviceable plane. It turned out to be a collectors item with on-line prices from $345 to $100+. Worth the trip.