Doi Inthanon National Park is located to the south of the city. This could easily be a day trip that can take you on a family outing, a couples get away or the perfect playground for the outdoorsy-type active hikers and trekkers. Trekking tours can be arranged through many agencies within the old city.
Within this mountainous park of wild species, you cannot find anywhere else in Thailand, you will come upon attractions such as Wachiratarn Waterfall, Sirithan Waterfall, King Inthanon Memorial Shrine, twin stupas dedicated to the King and Queen and the highest spot in Thailand.
I would recommend the necessities such as sunblock, mosquito repellent, a hat, sunglasses to protect your lovely selves and picnic items such as fruits, snacks and water in case you get thirsty and hungry. There’s also souvenir/cafeteria, visitor center and restrooms near the top.
Have fun exploring. You can explore via renting a motorbike, trekking tours, your rental car or by a taxi. Also see my post about 6 ways to get around Chiang Mai.