Currently 2 main airports serve Bansko, Sofia (around 160 km away) and Plovdiv (around 180 km away). A proposal for Bansko's own airport is currently well advanced, but no construction has yet started.
By train (from Greece)
Night trains leave from Athens and arrive to Blagoevgrad in the morning, via Thessaloniki. You can catch the train at Thessaloniki or any other station. The round trip ticket from Athens costs ~40€ (Christmas 2008), plus ~10€ for a bed in a 6-bed room for each trip. (60€ for the round trip with a bed in both trips). You should book tickets and beds in advance, especially during holiday seasons. From Blagoevgrad there is frequent bus service (every 30-60 minutes) to Bansko, the ticket costs 3-4 Leva. The bus station is very close to the train station, around 5 minutes on foot. From Bansko bus station you can call a taxi to your hotel, ask at the ticket office. You should agree on the price when you get in to avoid surprises (10-15 Leva should be enough). Some hotels may suggest a bus ride from Blagoevgrad to Bansko, at a much higher price though.
There are many buses departing Sofia each day from different stations so be sure to check which station your bus is departing from. Room for luggage can be an issue as they are mainly vans so you may have to wait for the next one on occasion if you have bulky items eg snowboard. The cost is around 15leva/7.5€ each way. The timetable can be found here. 
Getting around in Bansko is relatively easy. The town is not large, and walking around is nice. Taxis are relatively cheap (5-10 leva), though you should arrange the price beforehand. Have your hotel reception call you a taxi if you can. If you get to Bansko with your car, bear in mind that few roads get cleaned from the snow and ice, so snow chains may be required even in the city. Don't be fooled by local cars not using chains, as they use winter tyres which make a lot of difference! Renting a car from Sofia for most tourists is considerably beneficial because of the flexibility. Taxi rides can cost anywhere from 1-5 Euro per kilometer and are not recommended when traveling outside the city of Bankso. Buses run from Sofia and Blagoevgrad frequently during the winter (high season) and are the preferred method of travel for backpackers. The СОФИЯ - БАНСКО (Sofia - Bankso) is listed here in cryllic: 
In a nice day, with good visibility the view of the mountains is beautiful, especially if you take the lift to the ski tracks. (You should get to the ski tracks at least once even if you do not ski yourself)
Outside the winter season Bansko is a popular starting point for a number of hiking trips - in Pirin Mountains as well to the nearby Rila Mountains and Western Rhodope Mountains. There is also a number of mountain bike routes. In winter, except the resort skiing, the mountains around Bansko offer good conditions for ski touring, snowshoeing and cross-country skiing.
Bansko has a several tennis courts open to the public for free. There is a number of swimming pools that operate all the year round.
Bansko is a good place for skiing in winter and hiking in summer. The resort is mainly suited to beginners and those more advanced will get bored quite quickly. Also don't expect the runs to be groomed to often. Skiers and Snowboarders could find BanskoSki useful.  It is also a good idea to avoid any English school holidays as there will be insane amounts of people everywhere (and a 3 hour wait to get up the mountain via gondala) as well as the skiing world cup as half of the runs will be closed for the weeks leading up to it.
You can rent ski gear at the first station and get a discount at the lift ticket, though if you want to leave your skis there overnight there is an extra charge. A lot of ski rental shops can be found around the first station, where you can probably rent gear in better condition and get a good price if you book for more than 1 day (recommended) . (full ski gear for 4 days cost 100 leva - 50€). You can probably arrange to leave the gear at the shop overnight for free. The weather in Bansko is obviously colder than some Greek ski resorts, so warmer clothes and a full face hood is nice to have.
You can get a multiday ticket for the lifts, although the discount is negligible. There is also a half day ticket after 12:30 or 13:00 each day, but you can also buy tickets at a better price from people leaving the ski centre before the end of the day, around the ticket offices.
Most hotels offer a bus service to the ski lift station in the morning and afternoon. Try to get to the lift station not later than 9:00 to avoid long queues. It is also advisable to buy the tickets from the previous afternoon for the same reason. There are also minibuses to ferry people up the mountain in the morning which is included in the lift pass.
The hot thing to buy in Bansko at the moment is property. Several real estate agencies line the main road to the mountain, many of them aimed at English investors. Note, however, that prices are even higher than in the centre of Sofia.
There are some fashionable clothing retailers, as well as ski shops in the town. The prices for ski and sports gear are quite good, but usually not exceptional. You should be able to lower the initial price if you negotiate.
On a smaller budget, there are also numerous souvenir shops selling a range of generic Bulgarian items, as well as Bansko specific ones.
Bansko is rife with traditional Bulgarian taverns ('Mehana'; plural 'Mehani'), as well as cafes and modern bars along the main roads. Price should be around 10€ per person in most places. There are also a lot of places where you can get a slice of pizza or a sandwich. The "Friends Pub" near the first ski lift station is really nice, you can get a slice of pizza in the kiosk outside, or a full meal inside.The best tavern in Bansko is Matsurev han.The inn offers Bulgarian national cuisine, traditional dishes from Bansko, prepared on live coals, on a plate and in an oven. ”Matsurev’s Inn” is located at the foot of the Pirin mountain in the heart of the town of Bansko. It is located over the church “St. Trinity” at 100 m from the central square of the town and only at 15 minutes walking from the first station of the cabin lift.
By the end of the ski season (March-April) many restaurants offer large discounts to repeat customers too, sometimes up to 60% off, making eating out at this time incredibly cheap.
You can find nice 3-4 star hotels for ~€40 per night for a double room. Most hotels have sauna (free) and spa (extra charge). Belle vue is on of them, located near the ski lift station.