Hanging around in Phan Tiet can be more enjoyable than in the 10 km near Mui Ne Resort Strip because you will meet local people interested in you and you can go on and try to have a chat with them. Also, there won't be anyone trying to lure you into their shop or spa. Try local cuisine by just sitting down in any of the many food corners/street food stalls and wait for the dish to be prepared or try to gesticulate with hand gestures and basic English that you would want to have what the people around you are eating.
If you wish to explore the beach just south of Phan Thiet you will be almost completely be alone as there is a 20km long beach that stretches from the city to the light house of Ke Ga (10.704785, 107.986046). At the western end of the bay you can climb some dunes, although these are not as big as the ones north of Mui Ne but you will have them entirely to yourself (10.705278, 107.962074).
Phan Thiet hosts two big supermarkets which also offer some imported goods and products.
Co.opmart, 1 NGUYỄN TẤT THÀNH, Bình Hưng, tp. Phan Thiết, Bình Thuận, ☎ +84 62 3835440, . On the ground floor there is a Lotteria Burger, small bakery, and a three or four little open shops. On the third floor (top floor) there are a few arcade games and a food court (not recommended). Parking costs 1000VND and is in the open. All in all it's smaller than Lotte Mart. edit.
LOTTE Mart, Corner Hùng Vương to Tôn Đức Thắng (right at the roundabout), ☎ +84 62 3939 616, . 8:00 - 22:00. On the ground floor there is a Lotteria Burger, Pizza Hut, My Wu bakery, and Milano Coffee. Besides having a complete supermarket, the building also hosts a small bowling alley, an area for a few shops, a food court (not recommended) and a cinema that screens movies in English with Vietnamese subtitles. Parking your bike is for free. (10.938384,108.110510)edit
OC Saigon, 270 Ton Duc Thanh Street. Nice typically vietnamese cuisine and authentic loation. They have a wide choice of fresh seafood and other vietnamese meals!edit
Fresh spring rolls, 425 Trần Hưng Đạo Street (find it right in front of the scooter dealership in proximity of the Tran Hung Dao bridge. Just before the bridge when coming from Mui Ne). Have nice and authentic Vietnamese fresh spring rolls. You will receive a plate of mixed meat, a plate of herbs, salad and rice paper, and a little bowl with sauce to dip your self-rolled spring rolls in. It is street food rather than a restaurant as you will be sitting on typical Vietnamese little plastic stools. 30,000-40,000VND. edit
Local Seafood, Phạm Văn Đồng Street (On the northern side of the river just south of the Tran Hung Dao bridge. Across the river from the fish market). Along the whole street you can have nice Vietnamese seafood including clams, scallops, snails, squids, cuttlefish, shrimp, prawns, crabs, lobsters, sea cucumbers, and various types of fish. You will encounter young guys waving at you on the street trying to get you to eat at their establishment. Some restaurants have menus in English.edit
Love Sushi Lounge Cafe, 169-171 Ton Duc Thang (It is on the top floor of the white high rise building you see when facing your back towards the KFC), ☎ +84 122 300 4437, . 11:00-23:00. If you are keen on a cuisine other than the Vietnamese you might want to go here. It is a nicely decorated restaurant which actually serves good and tasty sushi. Prices are acceptable except if you are planning on going for the wine. Don't miss out on the 360° view over the city you can get on the rooftop! It's marked as "smoker area" and accessible by just going up the staircase one more floor.edit
Hai Nguyen Quan, Ton Duc Thanh Street (next to big Hotel Hong Long). Absolutelye genuine place - to chill with locals and enjoy there late night offers! They have got a big choice from beef to seafood, vegetables, even frogs! Try the beans!edit
Kim Trang Mini Hotel, 44 Hung Voung. Realy nice familiy iowned Guesthous with cheap and clean rooms with AC, Fan, TV and Bathroom. Double room coasts 250.000 VND triple room 350.000.edit
Thủ Khoa Huân st. after the cross with Tôn Đức Thắng st. is full of Guest Houses with price between 200.000VND and 300.000VND for 2 persons room. Almost every building is either a guesthouse, or a shop, or a barbershop, or etc.
By train: Phan Thiet has its own train station located at Cao Thắng street right in the city. It only serves one train though which leaves every day at 13:10 and arrives approximately 4 hours later in Ho Chi Minh City (Train Info). It only has soft and hard seats. To get on the Reunification Express you have to go to the Muong Man train station which is located 15km north-east from Phan Thiet (Muong Man; 10.968536|108.003630). Three Reunification Express trains going south and two going north stop there each day (Time table). The only way to get there is either by taxi or xe om(motorbike taxi which can be found in front of the co.op mart).
By Bus: Basically all open tour companies that go from Mui Ne to Ho Chi Minh City pass through Phan Thiet and therefore can take you with them if you buy a ticket and arrange everything in advance. So far the only open tour bus company office I found is the one from Hanh Cafe at 145 Thủ Khoa Huân.