What's a good strategy for determining the type of my pokemon's Hidden Power?

Pokemon Black and White has all new pokemon, and honestly, I'm not familiar enough with the game yet to tell you where you can find which pokemon. This is a problem, because I'm looking for a fast way to calculate Hidden Power in-game (I am aware that you can use IV calculators to determine what hidden power you have, but given the nature of IVs, you're outta luck for that method if your pokemon isn't already a reasonably high level and/or you've been keeping track of its EVs as well.)

Back in Emerald, for instance, I could reliably find Poochyena / Mightyena to test if Hidden Power was Psychic, Fighting/Bug, Dark/Ghost. I could then go find a Wurmple to determine if my Fighting/Bug result (super-effective against the Poochyena) was Fighting (also super-effective against the wurmple) or Bug (normal strength).

However, new version, new critters, my old plan no longer works; there aren't any poochyena in the game (or at least, not yet). Which common wild pokemon can I use to narrow down on the correct type of Hidden Power? (Assume I have access to Fly, and White, if it matters.)

In the more recent games, there are NPCs that you can talk to and they will tell you what type of Hidden Power your Pokémon has. According to Bulbapedia, the locations of the NPCs are:

• Platinum: Veilstone Game Corner
  • Prize Exchange
• Heart Gold/Soul Silver: Celadon Game Corner
  • Prize Exchange
• Black/White: Mistralton City
  • Pokémon Center.
• XY: Anistar City
  • South-Eastern-most house
  • Also the location of the Hidden Power TM.
• Omega Ruby/Alpha Sapphire: Fortree City
  • Top row of houses, second from the left.
  • Also the location of the Hidden Power TM

If you want to find out through combat, here's something I threw together (Disclaimer: there's likely a much more efficient way to figure it out):

1. Battle a Patrat / Lillipup.
Super effective: Fighting. Didn't affect: Ghost. Normal effectiveness: goto 2

2. Battle a Cottonee / Petilil.
Super effective: goto 3. Not very effective: goto 4. Normal effectiveness: goto 5.

3. Battle a Klink.
Super effective: Fire. Not very effective: goto 6. Didn't affect: Poison.

4. Battle a Roggenrola.
Super effective: goto 7. Normal effectiveness: Electric.

5. Battle a Sewaddle.
Super effective: Rock. Normal effectiveness: goto 8.

6. Battle a Woobat.
Super effective: goto 9. Normal effectiveness: goto 10.

7. Battle a Ducklett.
Normal effectiveness: Grass. Not very effective: Water. Didn't affect: Ground.

8. Battle a Sandile.
Normal effectiveness: goto 11. Not very effective: Dark. Didn't affect: Psychic.

9. Battle a Ferroseed.
Normal effectiveness: Ice. Not very effective: goto 12.

10. Battle a Timburr.
Super effective: Flying. Normal effectiveness: goto 13. Not very effective: Bug.

11. Battle a Darumaka.
Normal effectiveness: goto 14. Not very effective: Steel.

12. Battle a Drilbur.
Normal effectiveness: Dark. Not very effective: Rock.

13. Battle a Trubbish.
Normal effectiveness: goto 15. Not very effective: Poison.

14. Battle a Deino.
Super effective: Dragon. Normal effectiveness: Normal. Not very effective: Dark. Didn't affect: Psychic.

15. Battle a Blitzle.
Normal effectiveness: Dragon. Not very effective: Steel.

_{My thought process (possible types at each stage) is in the revision history of this answer.}

Kevin answered how to find out the type, however it should be noted that in generations 2-5 the base power of Hidden Power varies from 30 to 70 so it's not always a viable move in those games (a super-effective hidden power with power 30 is less powerful than a 'not very effective' Leaf Storm, for example).

There are a few ways to find out the power. One way to guess roughly is to battle and judge it based on other Special moves your Pokemon knows.

For example, I had an Ampharos with Power Gem (power 70) so I saved my game, taught it HP, then tried both moves on various wild Pokemon to gauge how effective it was. I ended up soft-resetting my game since the move was quite weak. Make sure to keep in mind any potential variations including power boosts from STAB (Same Type Attack Bonus), whether one of the types is super/not effective, and that wild Pokemon vary slightly in their stats.

The more accurate way is to use an IV Calculator like this one. Assuming you just caught a Pokemon (which therefore has 0 EVs) or you know exactly how many EVs it has, plug in your Pokemon's stats and click "Calculate Individual Values" then "Calculate Hidden Power". This should tell you the type and power of Hidden Power.