Hi Jeson! Welcome to ATP.
I started listing the ideas above that I thought were great, but I listed them all. Those guys are smart.
If you list a more detailed address, other ATP members who live near you can find you. Some day you might want to get together to swap seedlings, cuttings or plants if you can all meet at a big parking lot or fast food place.
Also, when you look at member's plant lists, sometimes they list them in categories like "have seeds to swap" or "want to swap plants". That way, you know the plants do well in your soil and climate, and you have a local source for advice.
I want to add a vote for checking out your neighbors' gardens. A knock on the door if they like surprises is a great way to make a gardening friend: praising someone's garden is like praising their children. Immediately they will know that you are wise and discerning.
I'm not so sure about walking onto their property and leaning over a fence. Admiring from the road is good, waving at them in the yard is good.
Leaving a note in a mailbox is the least intrusive way to introduce yourself. Not everyone likes having a stranger show up on their doorstep, knocking on the door.
A note saying you wish you could see their garden up close some day at their convenience, with your phone number and email is more likely to make a positive first impression on someone who is shy or territorial. And you can write it out before leaving home.
Many people do not bother with exact plant names and won't be able to tell you what exact cultivar or species something is. Some people get defensive if you ask for Latin names. take a photo and ask back here in the Plant ID forum!
They might offer you a cutting or a seed-head so you can grow it without ever knowing the name ... but some people are possessive of their prize plants.
You might want to wait a few visits before asking for favors like cuttings. Maybe wait until after you have something to offer them (seeds, compost, manure, leaves, clean pots, rooted cuttings or divisions of plants) or loan (like a wagon or watering plants while they're on vacation).
Asking for a cutting or division 2-3 visits AFTER you offered them some things is a classy way to avoid being thought of as pushy.
On the other hand, asking for advice like "How DO you get them to grow so big?" is more like giving them a gift, than asking for a favor!