We were in Basel just two nights. Its a beautiful and colorful city. You probably need to define "nice hotel". We stayed at the Motel One (NOT the U.S. chain). It was nice for us. We liked the location, the staff was nice and helpful and the room, fresh and spotless. For Switzerland, it was, I think, a good value. It was in what I'd consider the transit center. It was a great place to be to just walk around. It's by the cathedral. Another nice area might be where the historic town hall is location, which is also where there is a market, daily, I believe.
The Basel Tourist information office is excellent. They have a great website. I sent an email a few months in advance of our trip and they sent all kinds of information including maps for walking tours.
I'm not sure Basel has enough to do for a week, but you should be able do interesting day trips. Bern and Luzern come to mind.