I like oregano and thyme. The oregano dies back in winter but comes back from the roots, and the thyme stays green even through the winter. They might need a little more protection in the pot though (mine are in the ground). Someone else may have some others to add.

Chives or garlic chives for the pot.

My favorite of the herbs I grow is rosemary but it grows too big for a strawberry pot. I love it with lemon on chicken and with garlic on steak. Love to just grab it when I get the mail too. Love the smell.

I loved the look of a fully planted herb pot in books, so have tried to recreate it in 3 different strawberry pots with limited success as compared to other larger pots. Even if you put a PVC pipe with holes in it the pots limit growth and don't stay moist for the moist loving herbs.

We've tried rosemary, thyme, oregano, calendula, pansies, cilantro, parsley, garlic chives, and chamomile in strawberry pots. Thyme, oregano, & garlic chives remain. The others were either annuals, died, or were moved to in ground plantings because the pots limit the spreading habit of the herbs where they root along the stems later in summer.

Last year, I emptied 2 of my 3 to plant in the ground instead and those plants have tripled in size in comparison to what is in the pots. The strawberry pots get hot in sunshine & don't allow a lot of root room except for the top spots. Sedums are growing nicely in the 2 tall strawberry pots now.

The strawberry pot herbs were just not enough production to harvest all summer as well as have extra to freeze for winter. They are lovely when planted, just don't stay that way long. Takes daily watering July until fall rains.

We potted up herbs last year as gifts to family members into large patio planters divided into 3 groups:
heat loving better drainage: rosemary, lavendar, thyme
moist, rich: parsley, basil thai & sweet, onion chives, oreganos
moist, rich: pot in pot planted peppermint & spearmint
Oregano & thyme also planted in solo containers for gifts & for ourselves. These are all doing well except for the rosemary that got too cold.

Still the herbs in the ground are doing the best and are the ones with the largest harvest. The plants in my remaining 4 pocket strawberry pot are cute & tiny except for the thyme which has hung over the side.