Hennessey's Tavern La Jolla 7811 Herschel Ave, La Jolla, CA92037 Hennessey's Tavern is a restaurant and bar with numerous locations in the area, including one based on Herschel Avenue…More in La Jolla. The location offers a wide range of food options for breakfast, lunch and dinner, including burgers, sandwiches, salads, soups and desserts. Some menu options include fried calamari, fries, mixed green salad, club sandwich, tuna sandwich, chicken club, steak, grilled salmon, shepherd’s pie and much more. It also has an extensive drink list, including bloody Mary’s, Irish coffee, white wines, red wines, tequila and more. Various specials throughout the week include beer deals, wine deals, combos and happy hour deals.