Vannieres has already been mentioned. Excellent wines across the board.
Domaine de la Vivonne has not been mentioned. They have a cellar of beautifully aged wines at reasonable prices. It is 15 minutes from the center of town. There are few if any places where you can get well-aged Bandol and that alone makes it worth a stop.
I am happy with Bastide Blanche in either first or second tier. Have had only once one of their single vineyard bottlings, so donāt have a full picture, but always thought their regular Bandol is great.
So many wines mentioned in this thread that I love, including Chateau Simone and Clos Cibonne along with the Bandol producers (havenāt had Ray-Jane, though). Pradeaux is notable for being in the same family since before the French Revolution.
Chateau Ste Anne Cuvee Collection is first-tier red for me. And they make a nice CĆ“tes de Provence that is widely available and very well priced in restaurants, e.g., in the town of Bandol. The Marc is really good too but you wonāt find it outside the domaine.
There is a street parallel to and up the hill from the main street in Bandol that has a number of smaller better local restaurants.