Since the plants are available Spring/Fall and Summer/Fall I time it so my sim goes on vacation during the last week of Spring and the First week of Summer. I can usually get them with 3 days of Spring and 3 of Summer but I've done it so many times I just know where stuff spawns by now.
Just start in the rental area and give them time to grow while you fish or whatever or collect the bugs. Then move on to the National Forest.. let them grow and collect then move on to the Hermits Place .. when Summer hits do the rounds again.
Maybe read the first herbalism skill book to level 3 at least so that identifying them isn't a problem.. then again all the plants will look different in your inventory so you'll know at least that you got them all.