Hakuba is a small village-only 9,000 people in the summer, so facilities are somewhat limited. Having said that the basics are catered for-there are 3 supermarkets, 2 banks, 1 post office, plenty of restaurants and cafes, lots of convenience shops and a number of outdoor shops.
There are 2 banks in Hakuba, Hachijuni Bank (literally "82 Bank") which is a short walk uphill directly from the train station, and Nagano Bank (walk right as you come out of the train station and it is a 5 minutes walk on the right hand side). They will change travellers cheques and the like for you, but beware their opening hours-they close about 3pm. If you just need to withdraw cash from an ATM then the best option is the post office opposite the Nagano bank near the station (beware-you can only access it during normal business hours0, or the 7/11 convenience shops. The latter is in Echoland, and is open 24 hours making it really handy. The following photo is an actual one taken from the ATM in Echoland.
There are 3 supermarkets in Hakuba, Jusco (downhill about a 20 minute walk from Echoland on the same road as the train station), A Coop (uphill about a 5 minute walk from the station), and Appleland (about a 10 minute walk past the Post office ). Jusco is the most popular and is open until 11 pm at night. Besides the mandatory groceries there is also a clothing section. If you don't want to walk it you can catch the Genki Go bus at night from Echoland. There are many convenience shops in Hakuba, including a 24 hour 7/11 in Echoland, and one near the station.
There is only 1 post office in Hakuba, it is a 5 minute walk from the train station (walk right when you leave the station). It is open normal business hours and has an international ATM available for use during the same hours. If you just need stamps you can get them from convenience shops.
For general sports gear Yamatoya Sports next to the train station is the best bet. They have a good range of outdoor gear including snow boots, goggles, and skis. Not much in the way of boarding gear however. For boarding gear, there is a specialist boarding shop near the post office (The Boarding Co). For serious mountain gear go straight to Rapie which is a 100 m south of of Jusco supermarket on the main road. It has all the necessary equipment for mountaineering and backcountry ski/boarding such as avalanche beacons, helmets and so on.
There are 3 main pharmacies in town, the American drug store (near Rapie Mountain shop), Oota Chemist (diagnally opposite the station), and the one below A Coop supermarket just up from the station. You will have fun miming your medical condition to the staff if you do not speak Japanese!
There is only 1 gym worth mentioning, that is the Hakuba Alps Gym in Echoland. It has a great range of machines, treadmills and even Les Mills fitness classes to keep your body in shape. Particularly recommended is the Body Healing class 3 days a week which is a mix of yoga, pilates and tai chi-designed to keep your core strength and stretch your muscles. You can go as a casual visit (¥1500), or join on a monthly basis- cost is about ¥5,000 a month.