I’m afraid that according to Johtonian tradition, you shouldn’t seek out a legendary beast but rather allow it to come to you. This isn’t, of course, to say that you can’t; technology has evolved to the point where you can track practically any pokémon’s location through the pokédex, pokétch, or pokégear, provided you’ve seen those pokémon at least once. It’s just that it’s rather taboo to do so, and if you’re attempting to give thanks, I wouldn’t recommend it. Especially for a pokémon such as Raikou, which is known for its just disposition.
That having been said, many Johtonians use temples and shrines for this express purpose. If you aren’t a follower of the Johtonian belief, I would recommend visiting a temple; the sages there will help you learn the proper prayers to the legendary beasts. (It’s thought that certain prayers may be carried from areas of sacred ground to our wandering legendaries—or even the stationary but hidden ones—via an elaborate system of spirits. So even if you visit a temple that isn’t anywhere near where you first encountered Raikou, you may still be able to send your thanks through this system and be reasonably certain that the message would be received. Or at least, that’s what the sages will tell you. It’s actually more of a case of “it’s the thought that counts.”)
Alternatively, shrines—smaller, standalone structures, usually located in wooded areas—may be used to contact our kami, but these tend to be riskier. First and foremost, you need to leave an offering suitable for the legendary you wish to contact. As these are signs of respect towards beings more powerful than yourself, you quite obviously can’t leave just anything. Second, shrines are thought to be manned by spirits themselves, and sometimes, the spirits are mischievous and thus extremely dangerous. For example, there is a famous shrine located in the heart of Ilex Forest dedicated to Celebi. The entire forest itself is considered to be Celebi’s domain, and Celebi, a time-traveling legendary, is known to be rather capricious. Consequently, according to local legend, travelers who wander too deeply into the forest’s sacred grounds and travelers who leave the wrong kind of offering at the shrine have been known to disappear, never to be heard from again. Of course, whether or not you believe that is up to you, but all I can say is there is definitive proof that Celebi exists … so make of that what you will.
In any case, regardless of the risk, shrines tend to be the more direct route because you’re interacting directly with spirits. There are some shrines across Johto and Kanto dedicated specifically to the legendary beasts, but really, if you can find one devoted to Celebi, this will work just as well, so long as you make your intent clear and leave an offering for Celebi as well. (It’s said that Celebi is often happy to take offerings meant for one of the beasts to the beast in question, but it’s simply common courtesy to thank Celebi for doing so.)
Whatever your method for contacting the beasts, anonymous, just remember that what you’re dealing with is a regional legendary—one of the most important to a culture. As such, it’s imperative that you show the utmost respect towards Raikou as you thank it. Follow the sages’ advice to the letter or leave a generous offering, and never try to cross Raikou in the process—not even to catch it (unless it very clearly chooses you to be its trainer).
Good luck, anonymous!