While the Shizuoka Royal Hotel is a budget hotel, it doesn't have a tatami floor.
Here's some info on it:
SHIZUOKA ROYAL HOTEL
Address: Shizuoka Shi, Suehiro, 103-1
Tel.: (054)2711171
very reasonable decent hotel especially popular with small-budget sportsmen and students. A bit awat from town centre but easily reachable by bus from Shizuoka JR Station and within cheap taxi fare.