Boots of Springheel Jak
After you have fenced 900 gold worth of stuff, you'll get a journal update and Amusei will come looking for you again. Since your meeting with the Gray Fox is to take place in Cheydinhal, that's where Amusei will not search for you. If you just stay put in Chorral after completing the "Arrow of Extraction" quest, he should find you within a few hours (game-time).
You're going to be meeting at Ganredhel's house, which is on the east side of town, next door to the boarded up house that is the entrance to the Dark Brotherhood Sanctuary. Your easiest route will probably be to travel to the East Gate and just hop down the street from there. Ganredhel should be standing outside, so it shouldn't be too hard to find.
The Gray Fox needs you to steal the Boots of Springheel Jak, a thief who died about 300 years ago and was supposedly buried with his boots on. The Gray Fox can't give you much information to get you started other than that Jak has a decendant, Jakben, the Earl of Imble (Jack be nImble?), who lives in somewhere in the Imperial City. So start there and see what you can find.
The Earl of Imble lives in the Talos Plaza district. But while his house is fairly simple to find, the Earl himself is rather scarce most days. Breaking in is no big deal. If you do it at night, while Gemmlus Axius is asleep, you only have to worry about the Earl. If you're confronted by the Earl, he'll cower in fear and give you the key to the crypt if you ask about the boots. The boots aren't in the crypt, but it's a more private place to be conducting your business, so I opt for that rather than risking a confrontation in the house where the butler might get involved (Blood Price and all that). Waiting until later also avoids the possibility of a bounty attaching or attracting the attention of the Dark Brotherhood.
There is an Imble family genealogy in the desk upstairs. Note that the Earl will not summon the guards if all you do is take the key. If you tresspass in his private chamber, though, you'll pick up a small bounty and could get a guard on your heels. If you can make it to the crypt before he shows up, I'd recommend "Resist Arrest" as the better option since the crypt's occupants will take care of him for you and any subsequent guards will be after the occupants instead of you. That means that you can let the guards take care of the fighting and just clean up the goodies afterward. You can clear up your fine with Christophe or S'Krivva later.
So down to the basement you go and into the crypts. You'll find a few vampires down here, including a Vampire Matriarch/Patriarch. They're scattered, so taking them out one at a time is a good strategy. You'll find a lot of leveled goodies in the various coffins and such, but save Springheel Jak's coffin for last. It's in the small chamber just past the Matriarch/Patriarch.
As soon as you open it, you'll immediately notice something odd - no boots. But you can read the diary to find out why - Springheel Jak is still around. In fact, he's going to be standing behind you in a couple of seconds. Jakben, the Earl of Imble is Sprinheel Jak and is also a vampire. If you had managed to actually see his face during conversation, the red eyes and pointy canines would have clued you in on this. So take care of business and then retrieve the boots from his body (sorry, no vampire dust for those who may have completed the "Order of Virtuous Blood" quest). Once you've got the boots (they add 50 points to your Acrobatics skill) and whatever goodies you'd care to take with you, head for Cheydinhal to report back to the Gray Fox and complete the quest and collect your 500 gold.
The Gray Fox needs to spend some more time with Savilla's Stone, but believes he will have one last task for you soon.
If you have read the diary and have it in your inventory, you can gain some more Gray Fox trivia before you turn over the boots (after you give him the boots, the Gray Fox terminates the conversation and won't speak to you until the next mission):