Once you get onto Route 20, you're going to have to start fighting Trainers, who typically use Pokemon at a higher level than those found in the wild. You get more EXP for beating them, though, making it very rewarding to fight them. You also earn prize money.
The first Trainer you have to fight is a Youngster guarding the bridge. He has a Patrat L4 on his team. Further on is a Lass who uses a Purrloin L4. Go ahead and take the two of them out (they shouldn't be too tough) and then you'll be able to access a patch of tall grass. Inside of the tall grass is a Parlyz Heal. There's also another Youngster in there that uses a Patrat L4.
|Route 20 (Spring/Autumn/Winter)|
|Pidove||/||Lv. 2, 4||25%|
|Sewaddle||/||Lv. 2 ~ 4||35%|
|Purrloin||Lv. 3 ~ 4||15%|
|Route 20 (Summer)|
|Sunkern||Lv. 2 ~ 4||26%|
|Sewaddle||/||Lv. 2 ~ 4||35%|
|Purrloin||Lv. 3 ~ 4||14%|
The Pokemon you can find in the tall grass in certain areas varies by the season it is in the game. Remember, if your DS's clock's month is set to January, May, or September, it will be Spring; if it's set to February, June, or October, it will be Summer; if it's set to March, July, or November, it will be Autumn; and if it's set to April, August, or December, it will be Winter in your game. Thankfully, the only change here is Sunkern is a lot more common during the summertime, while it is comparatively rare elsewhere in the year. It will also be raining if it is Spring, so keep that in mind and avoid using Tepig's Fire-type attacks in the rain, as their power will be weakened.
New Pokemon to catch here are Sunkern, Sewaddle, and Pidove. Sewaddle is definitely the best of the three options, being a useful Bug/Grass-type that is capable of learning useful moves and has good stats when it evolves into Leavanny later on. It also picks up Bug Bite at level 8 and Razor Leaf and level 15, both of which are good options. Sunkern gets GrassWhistle at level 7 to help put the foe to sleep (although it's pretty inaccurate), Mega Drain at level 10, and Giga Drain at level 22. You need to use a Sun Stone to evolve it. Sunkern has very lousy stats, though, so keep that in mind (Sunflora is much better, albeit slow). Lastly Pidove is a rather unimpressive bird Pokemon. It lacks very powerful moves and stats, but it may still be worthwhile adding to your team if you like a bit of strategy.
Just past the patch of grass, there are some rocks scattered around. Press A while facing one of the rocks to pick up a hidden Poke Ball. The Hiker to the east won't let you pass until you've gotten your Gym Badge, so you're going to have to cross the bridge to the west instead.
Autumn Leaves a pleasant surprise!
During Autumn, the holes in the ground will be filled with leaves, granting you access to the areas otherwise inaccessible. You can cross the leaves across the bridge from the Hiker to find a free Poke Ball.
Over by the ledges, you can also take the pile of leaves northwest and then South, back into Floccesy Town. While it looks like it leads to a dead end, press A one step away from the bottommost tree to find a hidden Potion. Nifty!
When you get to the fork in the road, you can head west and then south to hop down some ledges in order to get back to Floccesy Town, or you can head north to enter the Floccesy Ranch. You may want to take this opportunity to go back and heal, but otherwise, make your way north to the Floccesy Ranch.