Muleshoe Bend - 7mi of bike trails, camping by/near the lake.
Pace Bend - roughly 3mi of bike trails, camping by/near lake
Mckinney Falls - 4mi of bike trails, camping in woods, some near the creek and waterfalls.
I don't know how serious of a biker you are but McKinney Falls' trails are REALLY easy. Perfect if you have kids though, or just want to putz around.
If you are hardcore, camp at Emma Long, and bike at City Park, which is really close by.. you can probably ride there but the hills are gnarly.