On the inside I will have 2 core switch running HSRP, these are already existing and working fine, when I configure a standby address on the inside interface of the ASA will I simply create another static route to that IP on the core to route traffic to that device in the even of a failure?
No, you will not create another route which points to the standby address. The standby address is just significant for the connectivity between the ASAs. In the case of a failover, the standby ASA will assume the IP of the active ASA as well as the MAC address, and the ASA which failed, when it comes back online will take the standby IP and will remain the standby ASA until you manually failover or a failover situation occurs on the new primary.
If this is the case I am assuming I will do the same on the outside interface if I can get the ISP to provide another physical layer 2 interface for me to connect directly to my devices, then I will create another default route to the next hop address in which I already route to.
I am not entirely sure I understand what you are asking here. As of right now you cannot have two active default routes on a single ASA. What you would need though is another connection to the standby ASA and a public IP that can be used as the standby IP, and the outside interface of the active and standby ASAs need to be on the same Layer2 network.
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