Where is a good place to start searching for raikou?

If you go to the top entrance of the cave east of Cerulean City, above the powerplant, there is a Pokemon center. Right above it there is a grass patch.

What I did was use max repel, put a level 50 or below Pokemon first in my party, and also had a Pokemon with HM02 Fly, and everytime I'd fly to that same Pokemon center, go up to the grass patch walk a little to see if Raikou is there, and if unsuccesful, I'd do it again and again. You'll find him eventually.

This is a very good place because you don't have to change routes from the Pokemon center to the grass patch. Raikou changes routes everytime you change routes or use Fly. When you finally find raikou, first use a status effect, I suggest you put him to sleep, or maybe paralyze him, but make sure your pokemon's speed is greater than 130 or so. He'll run away most likely after that.

Then, save the game just in case, and do the same thing, Fly everytime to the Pokemon center, but now you can track him down in your Pokedex entry everytime, to see where he's at. When you encounter him again, attack him until his hp is really low, but if you accidentally make him faint, turn off the game and start from the save point. If he runs, and he's still on the map, put save.

After his hp is really low, and he's asleep or paralyzed, you can try catching him with ultra balls, or you can use your Master Ball at the beginning if you still have it. If you use ultra balls, I suggest you use a wobuffet at a high level, because wobuffet's ability is shadow tag, and it doesn't let the enemy escape.

The only thing you have to watch out for now is Raikou using roar. If he uses roar anywhere in the process, DO NOT PUT SAVE, because he won't appear anywhere on the map anymore. In this case, turn off the game, and start from the last save point. Good luck, hope I helped. =)