Right near the start of the route, talk to the lady standing at the edge of the path and she'll give you TM94 (Rock Smash). That will definitely come in handy in your fight against the upcoming Normal-type Gym, that's for sure! Since it is no longer an HM move, you can replace it whenever you want, meaning it doesn't hurt at all if you teach it to your Pokemon for right now. Pokemon like Lillipup or Roggenrola, or even your starter will definitely benefit from having it.
Keep going down the path if you'd like. There's a Nurse you can battle who has a Munna L15, which may prove rather challenging for you due to its level. However, after beating her, she'll heal up your Pokemon. You can also talk to her at any point to have her heal your Pokemon, which saves you a few steps heading back to the Pokemon Center.
|Pinwheel Forest (Outer)|
|Tympole||Lv. 12 ~ 15||40%|
|Pidove||/||Lv. 12 ~ 13||30%|
|Timburr||Lv. 13 ~ 14||20%|
|Sawk||Lv. 12, 15||B: 10%
|Throh||Lv. 12, 15||B: 0%
|Tympole||Lv. 14 ~ 17||40%|
|Pidove||/||Lv. 14 ~ 15||30%|
|Timburr||Lv. 15 ~ 16||20%|
|Sawk||Lv. 14, 17||B: 10%
|Throh||Lv. 14, 17||B: 0%
|Shaking Grass / Swirling Dust||Level(s)||Rarity|
|Audino||Lv. 12 ~ 15||95%|
|Throh||Lv. 15||B: 5%
|Sawk||Lv. 15||B: 0%
Throughout Pokemon Black and White, you'll sometimes be able to find only certain Pokemon in one version and not in the other. Sometimes, you'll be able to find both in either version, but one is rarer or harder to come by than the other. In the table above, you'll see Sawk and Throh with different rarities depending on the version that's being played. "B" stands for Black while "W" stands for White. However, pay close attention to the "Rustling Grass / Dust Cloud" table — you can find the rarer of the two Fighting-type Pokemon only in the rustling grass!
Past the Nurse, there are a few Preschoolers that you can fight. There's also an Ether that can be reached by going inside of the gate near the Nurse. Anyway, back to the Preschoolers. One of them has a Cottonee L13 and a Petilil L13 while the other has a Roggenrola L14. Then, past the Preschoolers you'll find another Great Ball. Great.
Keep going south and you'll find even more tall grass, as well as a Youngster down there with some interesting Pokemon ready to battle. He has three Tympole at L13. Tympole is an odd little Water-type Pokemon, so be wary. Past him you can find an Antidote, then another Youngster to the east while some thick grass is over to the west. There's a Super Potion in the southeast corner of the thick grass, but that's about it, other than the Pokemon there. The second Youngster nearby has a Venipede L14, which is a big Bug-type Pokemon similar to Weedle back in the day, and he also has a Lillipup L14.
Head to the east and climb up those steps and you'll find a Black Belt and Battle Girl waiting up there. They each have a Timburr L16, which is a rather powerful Fighting-type Pokemon. Head down the steps by the Black Belt and you'll reach the Net Ball that was waiting up on that ledge. Yeah, really exciting. Ah well, hop off the ledge and then head west to the previous area, where you can either head back or go fight around in the thick grass in search of some rare Pokemon.
Once a day, if you have a Fighting-type Pokemon in your team, you can examine the big rock near the Black Belt and Battle Girl. You'll be able to smash part of the rock and break off a Star Piece, which can be sold for a respectable $4900. (Or you can sell them to the rare item collector in Icirrus City for a whopping $9800!)
Since the path into Pinwheel Forest is blocked off by Team Plasma for now, it's a good time for you to return to the Gym and get your 2nd Badge, now that you have all of this extra training under your belt!