Is there an option to run a single club with multiple shipping options? Example - fedex ground $20 and free local delivery? Or do I have to create a separate club for each?
I think it depends on what circumstances you want for each option.
If you the shipping option that is based on the circumstances of the order (address, contents) I think you could create a Shipping Strategy that automatically encompassed those reasons and set them. There might be limitations depending on how different the shipping options are.
If you were choosing the option (or asking each customer for their default) you could set the shipping option as an override in their club membership.
Another choice would be when processing the club - you could filter your club list in the club proces by certain circumstances (like ship state) and process in pieces with your chosen shipping option based on that.
Our client has club members that live out of the area but still in state that are shipped and the locals get free local delivery. Is that a possible scenario in which she can run in the same club without issue?
Probably the simplest way to run that is in the Club Membership - while setting their Shipping Options you could override strategy/type. If you create a separate shipping method for free local shipping you could apply it to locals only and it will apply only to club shipments.
However, I think that locals being local should be encouraged to pick up instead. I would definitely not recommend a policy that incentivizes your most likely visitors to stay home.