Mint is super easy to grow. My front yard is overrun by them since I made the mistake of putting it into the ground. I wish I had a contained area like Kahikina, that would have been more manageable. I didn't even buy my mint plant, it was a garnish on the side of my Vietnamese salad. I brought it home and stuck the sprig into water and it rooted, I planted it in my yard and now the suckers are popping up all over the place and I tear them out by the handfuls and throw them into my green waste because I have so much and none of my neighbors know what to do with them. Now that I'm into tiki drinks, though, I will not throw them away since I know they make the best garnish!
Another thing you may be able to grow is the Kaffir Lime. The leaves give off a very nice aroma when crushed and used a lot in Thai curries. The fruit smells simply amazing when you cut into it, it's like a lime with a vanilla smell. The lime doesn't have much juice but the leaves and the lime rind smells divine. Finger lime is much more rare, and the fruit is like a long finger filled with little lime balls that pop in your mouth, kind of like a mini-boba. It's subtly sour and adds a great texture. You could probably line a cocktail glass rim with Finger lime, or put it on your oysters/sushi/desserts.
Basil could be used in some drinks sparingly, I suppose, as lavender and it's flowers. I've seen the agastache flower stems used as a cocktail garnish on rareseeds.com
Hot chilis could be steeped into vodka, as with lemon grass.
I grow all of these in my garden except for the agastache and lavender - too hot in Hawaii, I think.