Basel is home to over 40 hotels across a broad range of price categories, so there should be somewhere to stay to suit all tastes and budgets. Virtually all Basel's hotels are centrally located, meaning that the city is easily explorable on foot from pretty much anywhere that you'll end up staying.
If you book in Basel, be sure to keep a copy of your confirmation on you if you're flying in to Basel-Mulhouse airport - this can provide you with free transport from the airport to the city, rather than having to pay on the bus. Almost all hotels in Basel give out the equivalent of travelcards for staying in the town, which entitle you to free transport throughout the town.
Rather than list them all here, the easiest thing to do is direct you to the Basel Tourist Website - which has an exhaustive list of where to stay, as well as online booking facilities.
Don't forget to check reviews of hotels on the ever-useful Tripadvisor, though - it can really help in separating the wheat from the chaff when it comes to where to stay.
Budget Accomadation
There are currently three hostels in town - the YMCA Hostel and the Basel City hostel, both of which are located right next to SBB train station, and the Basel Backpack, which is a few minutes walk to the south of the train station on Dornacherstrasse. Beds start from around €22 a night.
The Basel St Alban hostel is due to re-open in March 2010.
There is also an Easyhotel for those who like things cheap and cheerful, which is located next to the Conference Centre in the middle of town.