i don't think it matters where you kill him, but you get a bonus for killing him in a more populated area, that way he's "found faster". i just killed him as he was walking down a roadway outside of town. i didn't get my bonus but i still got a bounty in solitude. just make sure you plant the incriminating letter, that's all that really matters
I found him easiest to cap in Whiterun. As he's walking toward the town gates, it's easy to get a spot where you can hide from the shadows and shoot him down. For best results, have an invisibility potion to guzzle after you fire.
I got him in Windhelm. He was standing around the courtyard with a couple of guards nearby, so I used a bow. It was actually the first time I'd used a bow in this game. It brought him out through the entrace and I fought him in a corner. The guards didn't follow him out and apparently nobody spotted us fighting (or they didn't care). After it was over I just strolled casually out of town, whistling innocently.
I fast travel to Riften from Dragon's Reach as its the first place on his list.
I always find him in the Bee and Bard (On the PS3-have yet to get this far with DB on the PC) I rent a room to keep the stupid nosy Argonian from following me. I wait for him to go up to his room and then I kill him.
Collect bonus and a nice set of armor to show off to Astrid.