Named after the wispy, olive-green shrub, the Thompson Austin hotel’s spacious fourth-floor dining room— with its globe lights, rustic-looking wood floor, and earth tones—comes off more as a stylish den than a poolside lounge. You can meet for drinks (a great martini variation has dashes of herbed honey and lemon oil) and snacks (like smooth boiled-peanut hummus with roasted salsa verde and fabulous grilled bread). Or you can linger till dinner. The aptly named Big Ol’ Beef Rib, in a thick French onion gravy, could have fed a frat house (alas, one side was juicy and the other was dried out). A well-cooked salmon filet arrived awash in olive oil and herbs. Chocolate panna cotta, tricked out with pomegranate seeds and tahini “crunchies,” made a seductive finale.