There is no hotel close to the Alexandra Palace. There are places to stay down the hill by Wood Green tube stop (east of AP). I have had good luck finding them with booking.com. There may also be hotels west of AP.
However.... The Wood Green stop is on the Piccadilly line so I have stayed at hotels near other stops on that line. Heathrow Airport is also on the Piccadilly line. The Holborn and Russell Square stops are near the British Museum and other touristy places and not far from the Hurricane Room if you want to play some pool while you are there. In that area, and depending on your budget... Club Quarters Hotel Covent Garden and Thistle, Bloomsbury Park are good.
If you get an Oyster Card using the tube and the buses is very easy. Just put some money in it and tap it on the turnstile to enter (and leave for the tube). There is a bus from near the Wood Green station to Alexandra Palace if you are not into half-hour hikes uphill. Google Maps shows the routes.