I'm not into chemicals either but sometimes I've come upon a few old fashioned combos that work pretty well. I don't get much of anything except aphids here, but it could be that this little spray will work for a lot of things.
I either use essential oils of rosemary, peppermint and thyme and mix them with water enough so they'll spray easily, or if I don't have the oils I'll add some fresh leaves of those herbs to a cup or two of water and let it simmer for 20 minutes or so then strain it and spray that on. You can water it down a little if you need to as well. That combo will work on a lot many plants without doing damage.
So will a little soap and water, I usually use Dawn.
Sometimes just spraying with a garden hose will also help. The best thing would be to check out different plants that birds in your area love because the birds will for sure keep aphids away if you have them.
That's about all I know. If none of that is helpful you could always water down a little Neem Oil and spray.
Hope this helps a little and welcome to All Things Plants! Check out the forums, you'll find more that interest you, I'll bet.