If you want to get all the missions from the Battle Pass, you're going to have to get 100 local specialties in Mondstadt and Liyue every single week, for a total of 200! Not a big issue if you only collect a handful every 2/3 days, then wait for it to refresh and collect again. But you can also collect them all within a day if you're feeling bored, or in a rush to complete them on the final day. If you're feeling lazy, simply collect the first few locations shown for each region.
Having Klee and/or Qiqi can help with gathering these, because they have passives that marks the special items on your minimap to find them easily.
Use 2 anemo characters in the party so you get the Anemo elemental resonance (-15% stamina consumption, 10% movement speed, -5% skill CD), and Kaeya's passive (-20% sprinting stamina), and Barbara or Diona for their elemental skill that reduces stamina. Then use foods like Barbatos Ratatouille to reduce sprinting stamina even further. These effects stack so you can run longer and go to the farm locations faster.
For Mondstadt region, only Klee has the passive to show the local specialties.
There are roughly a total of 48 Valberries in Stormbearer Mountains + Stormbearer Point, and they're not that far apart. Use your vision (middle mouse button on PC, or the "eye" icon to the right of your minimap) to help see items that are interactable.
There are multiple small lamp grasses in each marked area. There's a total of 17 small lamp grass, and 3 calla lilies.
There are plenty of small lamp grasses scattered around the teleport waypoint in wolvendom. You can pick these up as you head towards the wolf weekly boss to finish 2 tasks in a day.
There are about 30 wolfhooks in the area close to the wolf colosseum. They can be somewhat spread apart, but if you have already picked up a lot of the items in the previous location, then you don't really need to pick every single wolfhooks here to reach 100.
Mondstadt Flower Shop
If you are willing to spend some Mora to get it done faster, Flora npc in Mondstadt sells 20 local specialty flowers that you can buy for 1000 per flower. Buying all the local specialty flower will cost you 20,000 Mora, and the items refreshes every 3 days. Sweet Flower is not considered a local specialty, so you don't need to buy that.
In Liyue region, Qiqi is the one with the passive that shows Liyue local specialties on the minimap.
Each Jueyun Chili plant has 3 chilies. There are 12 chilies in Qingce Village alone, so that totals to 36 in the area. Don't forget about the one close to the teleport waypoint on the left as well!
The paddy field north of Qingce Village has plenty of Glaze Lilies, scattered around. There are 13 shown in the picture above.
There are plenty of flowers that you can pick in Liyue Harbor, and all are on the grassy areas on the left side of the town. Start by going to the teleport waypoint and go to the area below to pick all the flowers, then head north near to herbalist shop.
In the herbalist shop, you can buy 10 Qingxin flowers for a +10 for the count. Similar to the flower shop in Mondstadt, this refreshes every 2~3 days.
Teleport to Wanshu Inn teleport waypoint, then jump down to the south area close to the bridge. Then pick up all the silk flowers that are in small bushes. These are quite easy to spot. Each bush has 2 silk flowers, so getting all of these will give you 14 easily.
Go to the teleport waypoint on the right of Mt. Aozang, and pick up the Jueyun Chilies on the left, then back to the teleport waypoint and climb up to get the ones up north.
Some extra ones that you can pick up. After going north from the last location, go back to the teleport waypoint, then head east to get the ones shown in the picture above.
Philanemo mushroom, dandelion seeds and windwheel aster work for monstadt local, and liyue has cor lapis and violet grass, can confirm all these work for BP points.