You do not give any idea of your budget, but if being central is a main concern, look at The Globe in the market place. Be aware that many of the hotels that pop up on TA and other sites as being in King;s Lynn are actually nowhere near Kings Lynn but out in rural Norfolk and you would need a car to get to them.
I'd agree The Globe, if that's the Wetherspoons Pub/Hotel is central, West Lynn is just over the river accessible by ferry or bus and may have something. The bus service towards Hunstanton depending on season can run up to 3-4 times an hour if that helps.
I've stayed in the Globe and recommend it. Its only disadvantage was poor/dear parking, but that won't trouble you.
The Bank House hotel is your best bet, as very central to town centre (10 min walk from trains) very nice location by river, with some rooms having great river views. The food in the restaurant is always fantastic, and staff very friendly. Room rates for single occupancy are about £80-90 but they might do a discount as you want 8 nights. Good Luck