The KOA in Eureka is nice with very friendly owners and is - without traffic - only about 20-25 minutes from downtown. It's typical KOA fare - the sites aren't huge, the bathrooms are clean, and it serves as a good base but not necessarily a destination. There is a small, old cemetery adjacent to the park that might be a bit off-putting to some visitors. Across Interstate 44 from the KOA is a Jellystone Resort; however, the sites there seemed small and difficult to access when we drove through once.
Babler is definitely very nice - we recommend it to out-of-towners - but, as you mentioned, is electric-only. If you require full hook-ups or W/E, the KOA in Eureka would be my recommendation.
Ben & Molly (but Ben never types, so it's always Molly