Foods to avoid: - Salt or sodium. Salt, or specifically the sodium in salt, is a major contributor to high blood pressure and heart disease. - Deli meat. Processed deli and lunch meats are often packed with sodium. - Frozen pizza. - Pickles. - Canned soups. - Canned tomato products. - Sugar. - Processed foods with trans or saturated fat. What's the best drink for high blood pressure? Best drinks to lower your blood pressure: Skimmed milk, low-fat dairy products like yogurt and skimmed milk; Tomato juice; Beet juice; Hibiscus tea; Pomegranate juice.